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

Extensions 1→N→G→Q→1 with N=C6 and Q=C7⋊D4

Direct product G=N×Q with N=C6 and Q=C7⋊D4
dρLabelID
C6×C7⋊D4168C6xC7:D4336,183

Semidirect products G=N:Q with N=C6 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C6⋊1(C7⋊D4) = C2×C7⋊D12φ: C7⋊D4/Dic7 → C2 ⊆ Aut C6168C6:1(C7:D4)336,159
C6⋊2(C7⋊D4) = C2×C21⋊D4φ: C7⋊D4/D14 → C2 ⊆ Aut C6168C6:2(C7:D4)336,157
C6⋊3(C7⋊D4) = C2×C21⋊7D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C6168C6:3(C7:D4)336,203

Non-split extensions G=N.Q with N=C6 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C6.1(C7⋊D4) = C7⋊D24φ: C7⋊D4/Dic7 → C2 ⊆ Aut C61684+C6.1(C7:D4)336,31
C6.2(C7⋊D4) = D12.D7φ: C7⋊D4/Dic7 → C2 ⊆ Aut C61684-C6.2(C7:D4)336,36
C6.3(C7⋊D4) = Dic6⋊D7φ: C7⋊D4/Dic7 → C2 ⊆ Aut C61684+C6.3(C7:D4)336,37
C6.4(C7⋊D4) = C7⋊Dic12φ: C7⋊D4/Dic7 → C2 ⊆ Aut C63364-C6.4(C7:D4)336,40
C6.5(C7⋊D4) = D42⋊C4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C6168C6.5(C7:D4)336,44
C6.6(C7⋊D4) = C42.Q8φ: C7⋊D4/Dic7 → C2 ⊆ Aut C6336C6.6(C7:D4)336,45
C6.7(C7⋊D4) = C21⋊D8φ: C7⋊D4/D14 → C2 ⊆ Aut C61684C6.7(C7:D4)336,29
C6.8(C7⋊D4) = C28.D6φ: C7⋊D4/D14 → C2 ⊆ Aut C61684C6.8(C7:D4)336,32
C6.9(C7⋊D4) = C42.D4φ: C7⋊D4/D14 → C2 ⊆ Aut C61684C6.9(C7:D4)336,33
C6.10(C7⋊D4) = C21⋊Q16φ: C7⋊D4/D14 → C2 ⊆ Aut C63364C6.10(C7:D4)336,38
C6.11(C7⋊D4) = D14⋊Dic3φ: C7⋊D4/D14 → C2 ⊆ Aut C6168C6.11(C7:D4)336,42
C6.12(C7⋊D4) = D6⋊Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C6168C6.12(C7:D4)336,43
C6.13(C7⋊D4) = Dic21⋊C4φ: C7⋊D4/D14 → C2 ⊆ Aut C6336C6.13(C7:D4)336,46
C6.14(C7⋊D4) = C42.4Q8φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C6336C6.14(C7:D4)336,98
C6.15(C7⋊D4) = C2.D84φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C6168C6.15(C7:D4)336,100
C6.16(C7⋊D4) = D4⋊D21φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C61684+C6.16(C7:D4)336,101
C6.17(C7⋊D4) = D4.D21φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C61684-C6.17(C7:D4)336,102
C6.18(C7⋊D4) = Q8⋊2D21φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C61684+C6.18(C7:D4)336,103
C6.19(C7⋊D4) = C21⋊7Q16φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C63364-C6.19(C7:D4)336,104
C6.20(C7⋊D4) = C42.38D4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C6168C6.20(C7:D4)336,105
C6.21(C7⋊D4) = C3×Dic7⋊C4central extension (φ=1)336C6.21(C7:D4)336,66
C6.22(C7⋊D4) = C3×D14⋊C4central extension (φ=1)168C6.22(C7:D4)336,68
C6.23(C7⋊D4) = C3×D4⋊D7central extension (φ=1)1684C6.23(C7:D4)336,69
C6.24(C7⋊D4) = C3×D4.D7central extension (φ=1)1684C6.24(C7:D4)336,70
C6.25(C7⋊D4) = C3×Q8⋊D7central extension (φ=1)1684C6.25(C7:D4)336,71
C6.26(C7⋊D4) = C3×C7⋊Q16central extension (φ=1)3364C6.26(C7:D4)336,72
C6.27(C7⋊D4) = C3×C23.D7central extension (φ=1)168C6.27(C7:D4)336,73

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁