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Showing content from https://en.wikipedia.org/wiki/Point_groups_in_four_dimensions below:

Point groups in four dimensions

[ ]: Symbol Order [1]⁺ 1.1 [1] = [ ] 2.1 [2,2,2]: Symbol Order [(2⁺,2⁺,2⁺,2⁺)]
= [2⁺,2⁺,2⁺]⁺ 1.1 [2⁺,2⁺,2⁺] 2.1 [2⁺,2,2⁺] 4.1 [(2,2)⁺,2⁺] 4 [[2⁺,2⁺,2⁺]] 4 [2,2,2]⁺ 8 [2⁺,2,2] 8.1 [(2,2)⁺,2] 8 [[2⁺,2,2⁺]] 8.1 [2,2,2] 16.1 [[2,2,2]]⁺ 16 [[2,2⁺,2]] 16 [[2,2,2]] 32 [p,2,2]: Symbol Order [p⁺,2,2⁺] 2p [(p,2)⁺,2⁺] 2p [p,2,2]⁺ 4p [p,2,2⁺] 4p [p⁺,2,2] 4p [(p,2)⁺,2] 4p [p,2,2] 8p [2p,2⁺,2]: Symbol Order [2p⁺,2⁺,2⁺]⁺ p [2p⁺,2⁺,2⁺] 2p [2p⁺,2⁺,2] 4p [2p⁺,(2,2)⁺] 4p [2p,(2,2)⁺] 8p [2p,2⁺,2] 8p [p,2,q]: Symbol Order [p⁺,2,q⁺] pq [p,2,q]⁺ 2pq [p⁺,2,q] 2pq [p,2,q] 4pq [(p,2)⁺,2q]: Symbol Order [(p,2)⁺,2q⁺] 2pq [(p,2)⁺,2q] 4pq [2p,2,2q]: Symbol Order [2p⁺,2⁺,2q⁺]⁺=
[(2p⁺,2⁺,2q⁺,2⁺)] pq [2p⁺,2⁺,2q⁺] 2pq [2p,2⁺,2q⁺] 4pq [((2p,2)⁺,(2q,2)⁺)] 4pq [2p,2⁺,2q] 8pq [[p,2,p]]: Symbol Order [[p⁺,2,p⁺]] 2p² [[p,2,p]]⁺ 4p² [[p,2,p]⁺] 4p² [[p,2,p]] 8p² [[2p,2,2p]]: Symbol Order [[(2p⁺,2⁺,2p⁺,2⁺)]] 2p² [[2p⁺,2⁺,2p⁺]] 4p² [[((2p,2)⁺,(2p,2)⁺)]] 8p² [[2p,2⁺,2p]] 16p² [3,3,2]: Symbol Order [(3,3)^Δ,2,1⁺]
≅ [2,2]⁺ 4 [(3,3)^Δ,2]
≅ [2,(2,2)⁺] 8 [(3,3)^⅄,2,1⁺]
≅ [4,2⁺] 8 [(3,3)⁺,2,1⁺]
= [3,3]⁺ 12.5 [(3,3)^⅄,2]
≅ [2,4,2⁺] 16 [3,3,2,1⁺]
= [3,3] 24 [(3,3)⁺,2] 24.10 [3,3,2]⁺ 24.10 [3,3,2] 48.36 [4,3,2]: Symbol Order [1⁺,4,3⁺,2,1⁺]
= [3,3]⁺ 12 [3⁺,4,2⁺] 24 [(3,4)⁺,2⁺] 24 [1⁺,4,3⁺,2]
= [(3,3)⁺,2] 24.10 [3⁺,4,2,1⁺]
= [3⁺,4] 24.10 [(4,3)⁺,2,1⁺]
= [4,3]⁺ 24.15 [1⁺,4,3,2,1⁺]
= [3,3] 24 [1⁺,4,(3,2)⁺]
= [3,3,2]⁺ 24 [3,4,2⁺] 48 [4,3⁺,2] 48.22 [4,(3,2)⁺] 48 [(4,3)⁺,2] 48.36 [1⁺,4,3,2]
= [3,3,2] 48.36 [4,3,2,1⁺]
= [4,3] 48.36 [4,3,2]⁺ 48.36 [4,3,2] 96.5 [5,3,2]: Symbol Order [(5,3)⁺,2,1⁺]
= [5,3]⁺ 60.13 [5,3,2,1⁺]
= [5,3] 120.2 [(5,3)⁺,2] 120.2 [5,3,2]⁺ 120.2 [5,3,2] 240 (nc) [3^1,1,1]: Symbol Order [3^1,1,1]^Δ
≅[[4,2⁺,4]]⁺ 32 [3^1,1,1]^⅄ 64 [3^1,1,1]⁺ 96.1 [3^1,1,1] 192.2 <[3,3^1,1]>
= [4,3,3] 384.1 [3[3^1,1,1]]
= [3,4,3] 1152.1 [3,3,3]: Symbol Order [3,3,3]⁺ 60.13 [3,3,3] 120.1 [[3,3,3]]⁺ 120.2 [[3,3,3]⁺] 120.1 [[3,3,3]] 240.1 [4,3,3]: Symbol Order [1⁺,4,(3,3)^Δ]
= [3^1,1,1]^Δ
≅[[4,2⁺,4]]⁺ 32 [4,(3,3)^Δ]
= [2⁺,4[2,2,2]⁺]
≅[[4,2⁺,4]] 64 [1⁺,4,(3,3)^⅄]
= [3^1,1,1]^⅄ 64 [1⁺,4,(3,3)⁺]
= [3^1,1,1]⁺ 96.1 [4,(3,3)^⅄]
≅ [[4,2,4]] 128 [1⁺,4,3,3]
= [3^1,1,1] 192.2 [4,(3,3)⁺] 192.1 [4,3,3]⁺ 192.3 [4,3,3] 384.1 [3,4,3]: Symbol Order [3⁺,4,3⁺] 288.1 [3,4,3^⅄]
= [4,3,3] 384.1 [3,4,3]⁺ 576.2 [3⁺,4,3] 576.1 [[3⁺,4,3⁺]] 576 (nc) [3,4,3] 1152.1 [[3,4,3]]⁺ 1152 (nc) [[3,4,3]⁺] 1152 (nc) [[3,4,3]] 2304 (nc)

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