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Extensions 1→N→G→Q→1 with N=C24 and Q=C2×C4

Direct product G=N×Q with N=C24 and Q=C2×C4
dρLabelID
C25×C4128C2^5xC4128,2319

Semidirect products G=N:Q with N=C24 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C24⋊1(C2×C4) = C24.78D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2416C2^4:1(C2xC4)128,630
C24⋊2(C2×C4) = C24.28D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4:2(C2xC4)128,645
C24⋊3(C2×C4) = C24.36D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4:3(C2xC4)128,853
C24⋊4(C2×C4) = C23.C24φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4:4(C2xC4)128,1615
C24⋊5(C2×C4) = C2×C2≀C4φ: C2×C4/C2 → C4 ⊆ Aut C2416C2^4:5(C2xC4)128,850
C24⋊6(C2×C4) = C22×C23⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4:6(C2xC4)128,1613
C24⋊7(C2×C4) = C25.C22φ: C2×C4/C2 → C22 ⊆ Aut C2416C2^4:7(C2xC4)128,621
C24⋊8(C2×C4) = C2×C23.23D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4:8(C2xC4)128,1019
C24⋊9(C2×C4) = C24.90D4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4:9(C2xC4)128,1040
C24⋊10(C2×C4) = C23.203C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4:10(C2xC4)128,1053
C24⋊11(C2×C4) = D4×C22⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4:11(C2xC4)128,1070
C24⋊12(C2×C4) = C23.240C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4:12(C2xC4)128,1090
C24⋊13(C2×C4) = C23.257C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4:13(C2xC4)128,1107
C24⋊14(C2×C4) = C2×C22.11C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4:14(C2xC4)128,2157
C24⋊15(C2×C4) = C4×C22≀C2φ: C2×C4/C4 → C2 ⊆ Aut C2432C2^4:15(C2xC4)128,1031
C24⋊16(C2×C4) = D4×C22×C4φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4:16(C2xC4)128,2154
C24⋊17(C2×C4) = C2×C24⋊3C4φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4:17(C2xC4)128,1009
C24⋊18(C2×C4) = C23×C22⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4:18(C2xC4)128,2151

Non-split extensions G=N.Q with N=C24 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C24.1(C2×C4) = C23⋊C8⋊C2φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.1(C2xC4)128,200
C24.2(C2×C4) = C42.395D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.2(C2xC4)128,201
C24.3(C2×C4) = C24.(C2×C4)φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.3(C2xC4)128,203
C24.4(C2×C4) = C42.372D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.4(C2xC4)128,205
C24.5(C2×C4) = C24.C23φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4.5(C2xC4)128,560
C24.6(C2×C4) = C24.6(C2×C4)φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4.6(C2xC4)128,561
C24.7(C2×C4) = C24.174C23φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.7(C2xC4)128,631
C24.8(C2×C4) = M4(2)⋊20D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.8(C2xC4)128,632
C24.9(C2×C4) = M4(2)⋊21D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4.9(C2xC4)128,646
C24.10(C2×C4) = C24.175C23φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.10(C2xC4)128,696
C24.11(C2×C4) = M4(2)⋊12D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.11(C2xC4)128,697
C24.12(C2×C4) = C42.115D4φ: C2×C4/C1 → C2×C4 ⊆ Aut C2432C2^4.12(C2xC4)128,699
C24.13(C2×C4) = C2≀C4⋊C2φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4.13(C2xC4)128,854
C24.14(C2×C4) = M4(2).24C23φ: C2×C4/C1 → C2×C4 ⊆ Aut C24168+C2^4.14(C2xC4)128,1620
C24.15(C2×C4) = C24⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C2416C2^4.15(C2xC4)128,48
C24.16(C2×C4) = C23.15M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.16(C2xC4)128,49
C24.17(C2×C4) = C23.2M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.17(C2xC4)128,58
C24.18(C2×C4) = C24.5D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.18(C2xC4)128,122
C24.19(C2×C4) = C42.371D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.19(C2xC4)128,190
C24.20(C2×C4) = C42.393D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.20(C2xC4)128,192
C24.21(C2×C4) = C25.3C4φ: C2×C4/C2 → C4 ⊆ Aut C2416C2^4.21(C2xC4)128,194
C24.22(C2×C4) = C42.42D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.22(C2xC4)128,196
C24.23(C2×C4) = C23⋊M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.23(C2xC4)128,197
C24.24(C2×C4) = C42.43D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.24(C2xC4)128,198
C24.25(C2×C4) = C4×C23⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.25(C2xC4)128,486
C24.26(C2×C4) = C4×C4.D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.26(C2xC4)128,487
C24.27(C2×C4) = C24.165C23φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.27(C2xC4)128,514
C24.28(C2×C4) = (C23×C4).C4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.28(C2xC4)128,517
C24.29(C2×C4) = C24.167C23φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.29(C2xC4)128,531
C24.30(C2×C4) = C42.96D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.30(C2xC4)128,532
C24.31(C2×C4) = C2×C23.D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.31(C2xC4)128,851
C24.32(C2×C4) = C4○C2≀C4φ: C2×C4/C2 → C4 ⊆ Aut C24164C2^4.32(C2xC4)128,852
C24.33(C2×C4) = C2×C23.C23φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.33(C2xC4)128,1614
C24.34(C2×C4) = C22×C4.D4φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.34(C2xC4)128,1617
C24.35(C2×C4) = C2×M4(2).8C22φ: C2×C4/C2 → C4 ⊆ Aut C2432C2^4.35(C2xC4)128,1619
C24.36(C2×C4) = C23.21C42φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.36(C2xC4)128,14
C24.37(C2×C4) = C24.4Q8φ: C2×C4/C2 → C22 ⊆ Aut C2416C2^4.37(C2xC4)128,36
C24.38(C2×C4) = C23.C42φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.38(C2xC4)128,37
C24.39(C2×C4) = C23.8C42φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.39(C2xC4)128,38
C24.40(C2×C4) = C23⋊2C42φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.40(C2xC4)128,169
C24.41(C2×C4) = C24.50D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.41(C2xC4)128,170
C24.42(C2×C4) = C24.5Q8φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.42(C2xC4)128,171
C24.43(C2×C4) = C24.52D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.43(C2xC4)128,172
C24.44(C2×C4) = C23.8M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.44(C2xC4)128,191
C24.45(C2×C4) = C24.45(C2×C4)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.45(C2xC4)128,204
C24.46(C2×C4) = C2×C23.9D4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.46(C2xC4)128,471
C24.47(C2×C4) = C23.15C42φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.47(C2xC4)128,474
C24.48(C2×C4) = C2×M4(2)⋊4C4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.48(C2xC4)128,475
C24.49(C2×C4) = C42.379D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.49(C2xC4)128,482
C24.50(C2×C4) = C23.17C42φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.50(C2xC4)128,485
C24.51(C2×C4) = C24.51(C2×C4)φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.51(C2xC4)128,512
C24.52(C2×C4) = C42.95D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.52(C2xC4)128,530
C24.53(C2×C4) = C24.53(C2×C4)φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.53(C2xC4)128,550
C24.54(C2×C4) = (C22×C4).276D4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.54(C2xC4)128,554
C24.55(C2×C4) = (C2×C8).195D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.55(C2xC4)128,583
C24.56(C2×C4) = C23.22M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.56(C2xC4)128,601
C24.57(C2×C4) = C23⋊2M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.57(C2xC4)128,602
C24.58(C2×C4) = (C2×C8)⋊D4φ: C2×C4/C2 → C22 ⊆ Aut C24164C2^4.58(C2xC4)128,623
C24.59(C2×C4) = M4(2).45D4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.59(C2xC4)128,633
C24.60(C2×C4) = C22⋊C4⋊4C8φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.60(C2xC4)128,655
C24.61(C2×C4) = C23.9M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.61(C2xC4)128,656
C24.62(C2×C4) = C42.325D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.62(C2xC4)128,686
C24.63(C2×C4) = C42.109D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.63(C2xC4)128,687
C24.64(C2×C4) = C23⋊C42φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.64(C2xC4)128,1005
C24.65(C2×C4) = C2×C24.C22φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.65(C2xC4)128,1021
C24.66(C2×C4) = C2×C24.3C22φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.66(C2xC4)128,1024
C24.67(C2×C4) = C23.191C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.67(C2xC4)128,1041
C24.68(C2×C4) = C23.194C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.68(C2xC4)128,1044
C24.69(C2×C4) = C24.91D4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.69(C2xC4)128,1047
C24.70(C2×C4) = C23.224C24φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.70(C2xC4)128,1074
C24.71(C2×C4) = M4(2)○2M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.71(C2xC4)128,1605
C24.72(C2×C4) = C2×(C22×C8)⋊C2φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.72(C2xC4)128,1610
C24.73(C2×C4) = C24.73(C2×C4)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.73(C2xC4)128,1611
C24.74(C2×C4) = D4○(C22⋊C8)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.74(C2xC4)128,1612
C24.75(C2×C4) = C42.257C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.75(C2xC4)128,1637
C24.76(C2×C4) = C2×C42.7C22φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.76(C2xC4)128,1651
C24.77(C2×C4) = C42.259C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.77(C2xC4)128,1653
C24.78(C2×C4) = C42.262C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.78(C2xC4)128,1656
C24.79(C2×C4) = C2×C8⋊6D4φ: C2×C4/C2 → C22 ⊆ Aut C2464C2^4.79(C2xC4)128,1660
C24.80(C2×C4) = C42.265C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.80(C2xC4)128,1662
C24.81(C2×C4) = M4(2)⋊22D4φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.81(C2xC4)128,1665
C24.82(C2×C4) = D4×M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.82(C2xC4)128,1666
C24.83(C2×C4) = C42.691C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.83(C2xC4)128,1704
C24.84(C2×C4) = C23⋊3M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.84(C2xC4)128,1705
C24.85(C2×C4) = D4⋊7M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.85(C2xC4)128,1706
C24.86(C2×C4) = C42.693C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.86(C2xC4)128,1707
C24.87(C2×C4) = C42.297C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.87(C2xC4)128,1708
C24.88(C2×C4) = C42.298C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.88(C2xC4)128,1709
C24.89(C2×C4) = C42.299C23φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.89(C2xC4)128,1710
C24.90(C2×C4) = C2×Q8○M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C2432C2^4.90(C2xC4)128,2304
C24.91(C2×C4) = C24.17Q8φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.91(C2xC4)128,165
C24.92(C2×C4) = C23.29C42φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.92(C2xC4)128,461
C24.93(C2×C4) = C8×C22⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.93(C2xC4)128,483
C24.94(C2×C4) = C23.36C42φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.94(C2xC4)128,484
C24.95(C2×C4) = C23.21M4(2)φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.95(C2xC4)128,582
C24.96(C2×C4) = C2×C23.8Q8φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.96(C2xC4)128,1018
C24.97(C2×C4) = C2×C8○2M4(2)φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.97(C2xC4)128,1604
C24.98(C2×C4) = C2×C42.6C22φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.98(C2xC4)128,1636
C24.99(C2×C4) = D4×C2×C8φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.99(C2xC4)128,1658
C24.100(C2×C4) = C2×C8⋊9D4φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.100(C2xC4)128,1659
C24.101(C2×C4) = C42.264C23φ: C2×C4/C4 → C2 ⊆ Aut C2432C2^4.101(C2xC4)128,1661
C24.102(C2×C4) = C22×C8○D4φ: C2×C4/C4 → C2 ⊆ Aut C2464C2^4.102(C2xC4)128,2303
C24.103(C2×C4) = C23.19C42φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.103(C2xC4)128,12
C24.104(C2×C4) = C2×C23⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.104(C2xC4)128,188
C24.105(C2×C4) = C2×C22.M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.105(C2xC4)128,189
C24.106(C2×C4) = (C2×C4)⋊M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.106(C2xC4)128,195
C24.107(C2×C4) = C23.28C42φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.107(C2xC4)128,460
C24.108(C2×C4) = C2×C22.C42φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.108(C2xC4)128,473
C24.109(C2×C4) = C4×C22⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.109(C2xC4)128,480
C24.110(C2×C4) = C42.378D4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.110(C2xC4)128,481
C24.111(C2×C4) = C24⋊3C8φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.111(C2xC4)128,511
C24.112(C2×C4) = C25⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C2416C2^4.112(C2xC4)128,513
C24.113(C2×C4) = C25.C4φ: C2×C4/C22 → C2 ⊆ Aut C2416C2^4.113(C2xC4)128,515
C24.114(C2×C4) = C4.C22≀C2φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.114(C2xC4)128,516
C24.115(C2×C4) = C42.425D4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.115(C2xC4)128,529
C24.116(C2×C4) = C23.32M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.116(C2xC4)128,549
C24.117(C2×C4) = C24.68D4φ: C2×C4/C22 → C2 ⊆ Aut C2416C2^4.117(C2xC4)128,551
C24.118(C2×C4) = (C22×C4).275D4φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.118(C2xC4)128,553
C24.119(C2×C4) = C2×C4×C22⋊C4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.119(C2xC4)128,1000
C24.120(C2×C4) = C2×C23.7Q8φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.120(C2xC4)128,1010
C24.121(C2×C4) = C2×C23.34D4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.121(C2xC4)128,1011
C24.122(C2×C4) = C25.85C22φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.122(C2xC4)128,1012
C24.123(C2×C4) = C2×C4×M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.123(C2xC4)128,1603
C24.124(C2×C4) = C22×C22⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.124(C2xC4)128,1608
C24.125(C2×C4) = C2×C24.4C4φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.125(C2xC4)128,1609
C24.126(C2×C4) = C22×C4.10D4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.126(C2xC4)128,1618
C24.127(C2×C4) = C2×C4⋊M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.127(C2xC4)128,1635
C24.128(C2×C4) = C2×C42.12C4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.128(C2xC4)128,1649
C24.129(C2×C4) = C2×C42.6C4φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.129(C2xC4)128,1650
C24.130(C2×C4) = C42.677C23φ: C2×C4/C22 → C2 ⊆ Aut C2432C2^4.130(C2xC4)128,1652
C24.131(C2×C4) = C22×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.131(C2xC4)128,2153
C24.132(C2×C4) = C23×M4(2)φ: C2×C4/C22 → C2 ⊆ Aut C2464C2^4.132(C2xC4)128,2302
C24.133(C2×C4) = C2×C22.7C42central extension (φ=1)128C2^4.133(C2xC4)128,459
C24.134(C2×C4) = C22×C2.C42central extension (φ=1)128C2^4.134(C2xC4)128,998
C24.135(C2×C4) = C22×C8⋊C4central extension (φ=1)128C2^4.135(C2xC4)128,1602
C24.136(C2×C4) = C22×C4⋊C8central extension (φ=1)128C2^4.136(C2xC4)128,1634
C24.137(C2×C4) = C23×C4⋊C4central extension (φ=1)128C2^4.137(C2xC4)128,2152

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