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

Extensions 1→N→G→Q→1 with N=C4 and Q=C22⋊C4

Direct product G=N×Q with N=C4 and Q=C22⋊C4
dρLabelID
C4×C22⋊C432C4xC2^2:C464,58

Semidirect products G=N:Q with N=C4 and Q=C22⋊C4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C22⋊C4) = C24.3C22φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C432C4:1(C2^2:C4)64,71
C4⋊2(C22⋊C4) = C23.7Q8φ: C22⋊C4/C23 → C2 ⊆ Aut C432C4:2(C2^2:C4)64,61

Non-split extensions G=N.Q with N=C4 and Q=C22⋊C4
extensionφ:Q→Aut NdρLabelID
C4.1(C22⋊C4) = C2.D16φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C432C4.1(C2^2:C4)64,38
C4.2(C22⋊C4) = C2.Q32φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C464C4.2(C2^2:C4)64,39
C4.3(C22⋊C4) = D8.C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C4322C4.3(C2^2:C4)64,40
C4.4(C22⋊C4) = D8⋊2C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C4164C4.4(C2^2:C4)64,41
C4.5(C22⋊C4) = M5(2)⋊C2φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C4164+C4.5(C2^2:C4)64,42
C4.6(C22⋊C4) = C8.17D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C4324-C4.6(C2^2:C4)64,43
C4.7(C22⋊C4) = C23.67C23φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C464C4.7(C2^2:C4)64,72
C4.8(C22⋊C4) = (C22×C8)⋊C2φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C432C4.8(C2^2:C4)64,89
C4.9(C22⋊C4) = C23.C23φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C4164C4.9(C2^2:C4)64,91
C4.10(C22⋊C4) = C2×C4.D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C416C4.10(C2^2:C4)64,92
C4.11(C22⋊C4) = C2×C4.10D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C432C4.11(C2^2:C4)64,93
C4.12(C22⋊C4) = C2×D4⋊C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C432C4.12(C2^2:C4)64,95
C4.13(C22⋊C4) = C2×Q8⋊C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C464C4.13(C2^2:C4)64,96
C4.14(C22⋊C4) = C23.37D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C416C4.14(C2^2:C4)64,99
C4.15(C22⋊C4) = C23.38D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C432C4.15(C2^2:C4)64,100
C4.16(C22⋊C4) = C2×C4≀C2φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C416C4.16(C2^2:C4)64,101
C4.17(C22⋊C4) = C4.9C42φ: C22⋊C4/C23 → C2 ⊆ Aut C4164C4.17(C2^2:C4)64,18
C4.18(C22⋊C4) = C4.10C42φ: C22⋊C4/C23 → C2 ⊆ Aut C4164C4.18(C2^2:C4)64,19
C4.19(C22⋊C4) = C22.4Q16φ: C22⋊C4/C23 → C2 ⊆ Aut C464C4.19(C2^2:C4)64,21
C4.20(C22⋊C4) = C4.C42φ: C22⋊C4/C23 → C2 ⊆ Aut C432C4.20(C2^2:C4)64,22
C4.21(C22⋊C4) = C22.C42φ: C22⋊C4/C23 → C2 ⊆ Aut C432C4.21(C2^2:C4)64,24
C4.22(C22⋊C4) = M4(2)⋊4C4φ: C22⋊C4/C23 → C2 ⊆ Aut C4164C4.22(C2^2:C4)64,25
C4.23(C22⋊C4) = C24.4C4φ: C22⋊C4/C23 → C2 ⊆ Aut C416C4.23(C2^2:C4)64,88
C4.24(C22⋊C4) = C23.36D4φ: C22⋊C4/C23 → C2 ⊆ Aut C432C4.24(C2^2:C4)64,98
C4.25(C22⋊C4) = C42⋊C22φ: C22⋊C4/C23 → C2 ⊆ Aut C4164C4.25(C2^2:C4)64,102
C4.26(C22⋊C4) = C22.7C42central extension (φ=1)64C4.26(C2^2:C4)64,17
C4.27(C22⋊C4) = C42⋊6C4central extension (φ=1)16C4.27(C2^2:C4)64,20
C4.28(C22⋊C4) = C22⋊C16central extension (φ=1)32C4.28(C2^2:C4)64,29
C4.29(C22⋊C4) = C23.C8central extension (φ=1)164C4.29(C2^2:C4)64,30
C4.30(C22⋊C4) = D4.C8central extension (φ=1)322C4.30(C2^2:C4)64,31
C4.31(C22⋊C4) = C2×C22⋊C8central extension (φ=1)32C4.31(C2^2:C4)64,87
C4.32(C22⋊C4) = M4(2).8C22central extension (φ=1)164C4.32(C2^2:C4)64,94
C4.33(C22⋊C4) = C23.24D4central extension (φ=1)32C4.33(C2^2:C4)64,97

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁