Home
About
Cn
Dn
Sn
An
Degree
Linear
Irr Reps
Characters
×
⋊
.
○
≀

Extensions 1→N→G→Q→1 with N=C12 and Q=C5×D4

Direct product G=N×Q with N=C12 and Q=C5×D4
dρLabelID
D4×C60240D4xC60480,923

Semidirect products G=N:Q with N=C12 and Q=C5×D4
extensionφ:Q→Aut NdρLabelID
C12⋊1(C5×D4) = C5×C12⋊D4φ: C5×D4/C10 → C22 ⊆ Aut C12240C12:1(C5xD4)480,774
C12⋊2(C5×D4) = C5×D6⋊3D4φ: C5×D4/C10 → C22 ⊆ Aut C12240C12:2(C5xD4)480,817
C12⋊3(C5×D4) = C5×C12⋊3D4φ: C5×D4/C10 → C22 ⊆ Aut C12240C12:3(C5xD4)480,819
C12⋊4(C5×D4) = C5×C4⋊D12φ: C5×D4/C20 → C2 ⊆ Aut C12240C12:4(C5xD4)480,753
C12⋊5(C5×D4) = C20×D12φ: C5×D4/C20 → C2 ⊆ Aut C12240C12:5(C5xD4)480,752
C12⋊6(C5×D4) = C15×C4⋊1D4φ: C5×D4/C20 → C2 ⊆ Aut C12240C12:6(C5xD4)480,932
C12⋊7(C5×D4) = C5×C12⋊7D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12:7(C5xD4)480,809
C12⋊8(C5×D4) = C20×C3⋊D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12:8(C5xD4)480,807
C12⋊9(C5×D4) = C15×C4⋊D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12:9(C5xD4)480,926

Non-split extensions G=N.Q with N=C12 and Q=C5×D4
extensionφ:Q→Aut NdρLabelID
C12.1(C5×D4) = C5×C6.D8φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.1(C5xD4)480,128
C12.2(C5×D4) = C5×C6.SD16φ: C5×D4/C10 → C22 ⊆ Aut C12480C12.2(C5xD4)480,129
C12.3(C5×D4) = C5×C3⋊D16φ: C5×D4/C10 → C22 ⊆ Aut C122404C12.3(C5xD4)480,145
C12.4(C5×D4) = C5×D8.S3φ: C5×D4/C10 → C22 ⊆ Aut C122404C12.4(C5xD4)480,146
C12.5(C5×D4) = C5×C8.6D6φ: C5×D4/C10 → C22 ⊆ Aut C122404C12.5(C5xD4)480,147
C12.6(C5×D4) = C5×C3⋊Q32φ: C5×D4/C10 → C22 ⊆ Aut C124804C12.6(C5xD4)480,148
C12.7(C5×D4) = C5×D4⋊Dic3φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.7(C5xD4)480,151
C12.8(C5×D4) = C5×C12.D4φ: C5×D4/C10 → C22 ⊆ Aut C121204C12.8(C5xD4)480,152
C12.9(C5×D4) = C5×Q8⋊2Dic3φ: C5×D4/C10 → C22 ⊆ Aut C12480C12.9(C5xD4)480,154
C12.10(C5×D4) = C5×C12.10D4φ: C5×D4/C10 → C22 ⊆ Aut C122404C12.10(C5xD4)480,155
C12.11(C5×D4) = C5×C4.D12φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.11(C5xD4)480,776
C12.12(C5×D4) = C5×C8⋊D6φ: C5×D4/C10 → C22 ⊆ Aut C121204C12.12(C5xD4)480,787
C12.13(C5×D4) = C5×C8.D6φ: C5×D4/C10 → C22 ⊆ Aut C122404C12.13(C5xD4)480,788
C12.14(C5×D4) = C10×D4⋊S3φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.14(C5xD4)480,810
C12.15(C5×D4) = C5×D12⋊6C22φ: C5×D4/C10 → C22 ⊆ Aut C121204C12.15(C5xD4)480,811
C12.16(C5×D4) = C10×D4.S3φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.16(C5xD4)480,812
C12.17(C5×D4) = C5×C23.12D6φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.17(C5xD4)480,815
C12.18(C5×D4) = C10×Q8⋊2S3φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.18(C5xD4)480,820
C12.19(C5×D4) = C5×Q8.11D6φ: C5×D4/C10 → C22 ⊆ Aut C122404C12.19(C5xD4)480,821
C12.20(C5×D4) = C10×C3⋊Q16φ: C5×D4/C10 → C22 ⊆ Aut C12480C12.20(C5xD4)480,822
C12.21(C5×D4) = C5×Dic3⋊Q8φ: C5×D4/C10 → C22 ⊆ Aut C12480C12.21(C5xD4)480,823
C12.22(C5×D4) = C5×D6⋊3Q8φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.22(C5xD4)480,825
C12.23(C5×D4) = C5×C12.23D4φ: C5×D4/C10 → C22 ⊆ Aut C12240C12.23(C5xD4)480,826
C12.24(C5×D4) = C5×D48φ: C5×D4/C20 → C2 ⊆ Aut C122402C12.24(C5xD4)480,118
C12.25(C5×D4) = C5×C48⋊C2φ: C5×D4/C20 → C2 ⊆ Aut C122402C12.25(C5xD4)480,119
C12.26(C5×D4) = C5×Dic24φ: C5×D4/C20 → C2 ⊆ Aut C124802C12.26(C5xD4)480,120
C12.27(C5×D4) = C5×C12⋊2Q8φ: C5×D4/C20 → C2 ⊆ Aut C12480C12.27(C5xD4)480,748
C12.28(C5×D4) = C5×C42⋊7S3φ: C5×D4/C20 → C2 ⊆ Aut C12240C12.28(C5xD4)480,754
C12.29(C5×D4) = C10×C24⋊C2φ: C5×D4/C20 → C2 ⊆ Aut C12240C12.29(C5xD4)480,781
C12.30(C5×D4) = C10×D24φ: C5×D4/C20 → C2 ⊆ Aut C12240C12.30(C5xD4)480,782
C12.31(C5×D4) = C10×Dic12φ: C5×D4/C20 → C2 ⊆ Aut C12480C12.31(C5xD4)480,784
C12.32(C5×D4) = C5×C12⋊C8φ: C5×D4/C20 → C2 ⊆ Aut C12480C12.32(C5xD4)480,123
C12.33(C5×D4) = C5×C42⋊4S3φ: C5×D4/C20 → C2 ⊆ Aut C121202C12.33(C5xD4)480,124
C12.34(C5×D4) = C5×C24.C4φ: C5×D4/C20 → C2 ⊆ Aut C122402C12.34(C5xD4)480,138
C12.35(C5×D4) = C5×C4○D24φ: C5×D4/C20 → C2 ⊆ Aut C122402C12.35(C5xD4)480,783
C12.36(C5×D4) = C15×D16φ: C5×D4/C20 → C2 ⊆ Aut C122402C12.36(C5xD4)480,214
C12.37(C5×D4) = C15×SD32φ: C5×D4/C20 → C2 ⊆ Aut C122402C12.37(C5xD4)480,215
C12.38(C5×D4) = C15×Q32φ: C5×D4/C20 → C2 ⊆ Aut C124802C12.38(C5xD4)480,216
C12.39(C5×D4) = C15×C4.4D4φ: C5×D4/C20 → C2 ⊆ Aut C12240C12.39(C5xD4)480,929
C12.40(C5×D4) = C15×C4⋊Q8φ: C5×D4/C20 → C2 ⊆ Aut C12480C12.40(C5xD4)480,933
C12.41(C5×D4) = D8×C30φ: C5×D4/C20 → C2 ⊆ Aut C12240C12.41(C5xD4)480,937
C12.42(C5×D4) = SD16×C30φ: C5×D4/C20 → C2 ⊆ Aut C12240C12.42(C5xD4)480,938
C12.43(C5×D4) = Q16×C30φ: C5×D4/C20 → C2 ⊆ Aut C12480C12.43(C5xD4)480,939
C12.44(C5×D4) = C5×C2.Dic12φ: C5×D4/C2×C10 → C2 ⊆ Aut C12480C12.44(C5xD4)480,135
C12.45(C5×D4) = C5×C2.D24φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12.45(C5xD4)480,140
C12.46(C5×D4) = C5×C12.46D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C121204C12.46(C5xD4)480,142
C12.47(C5×D4) = C5×C12.47D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C122404C12.47(C5xD4)480,143
C12.48(C5×D4) = C5×C12.48D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12.48(C5xD4)480,803
C12.49(C5×D4) = C5×D4⋊D6φ: C5×D4/C2×C10 → C2 ⊆ Aut C121204C12.49(C5xD4)480,828
C12.50(C5×D4) = C5×Q8.14D6φ: C5×D4/C2×C10 → C2 ⊆ Aut C122404C12.50(C5xD4)480,830
C12.51(C5×D4) = C5×Dic3⋊C8φ: C5×D4/C2×C10 → C2 ⊆ Aut C12480C12.51(C5xD4)480,133
C12.52(C5×D4) = C5×D6⋊C8φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12.52(C5xD4)480,139
C12.53(C5×D4) = C5×C12.53D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C122404C12.53(C5xD4)480,141
C12.54(C5×D4) = C5×D12⋊C4φ: C5×D4/C2×C10 → C2 ⊆ Aut C121204C12.54(C5xD4)480,144
C12.55(C5×D4) = C5×C12.55D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12.55(C5xD4)480,149
C12.56(C5×D4) = C5×Q8⋊3Dic3φ: C5×D4/C2×C10 → C2 ⊆ Aut C121204C12.56(C5xD4)480,156
C12.57(C5×D4) = C5×Q8.13D6φ: C5×D4/C2×C10 → C2 ⊆ Aut C122404C12.57(C5xD4)480,829
C12.58(C5×D4) = C15×C4.D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C121204C12.58(C5xD4)480,203
C12.59(C5×D4) = C15×C4.10D4φ: C5×D4/C2×C10 → C2 ⊆ Aut C122404C12.59(C5xD4)480,204
C12.60(C5×D4) = C15×D4⋊C4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12.60(C5xD4)480,205
C12.61(C5×D4) = C15×Q8⋊C4φ: C5×D4/C2×C10 → C2 ⊆ Aut C12480C12.61(C5xD4)480,206
C12.62(C5×D4) = C15×C22⋊Q8φ: C5×D4/C2×C10 → C2 ⊆ Aut C12240C12.62(C5xD4)480,927
C12.63(C5×D4) = C15×C8⋊C22φ: C5×D4/C2×C10 → C2 ⊆ Aut C121204C12.63(C5xD4)480,941
C12.64(C5×D4) = C15×C8.C22φ: C5×D4/C2×C10 → C2 ⊆ Aut C122404C12.64(C5xD4)480,942
C12.65(C5×D4) = C15×C22⋊C8central extension (φ=1)240C12.65(C5xD4)480,201
C12.66(C5×D4) = C15×C4≀C2central extension (φ=1)1202C12.66(C5xD4)480,207
C12.67(C5×D4) = C15×C4⋊C8central extension (φ=1)480C12.67(C5xD4)480,208
C12.68(C5×D4) = C15×C8.C4central extension (φ=1)2402C12.68(C5xD4)480,211
C12.69(C5×D4) = C15×C4○D8central extension (φ=1)2402C12.69(C5xD4)480,940

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁