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

Extensions 1→N→G→Q→1 with N=C4 and Q=C4⋊C8

Direct product G=N×Q with N=C4 and Q=C4⋊C8
dρLabelID
C4×C4⋊C8128C4xC4:C8128,498

Semidirect products G=N:Q with N=C4 and Q=C4⋊C8
extensionφ:Q→Aut NdρLabelID
C4⋊1(C4⋊C8) = C42⋊9C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4:1(C4:C8)128,574
C4⋊2(C4⋊C8) = C42.61Q8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C4128C4:2(C4:C8)128,671

Non-split extensions G=N.Q with N=C4 and Q=C4⋊C8
extensionφ:Q→Aut NdρLabelID
C4.1(C4⋊C8) = C42⋊1C8φ: C4⋊C8/C42 → C2 ⊆ Aut C432C4.1(C4:C8)128,6
C4.2(C4⋊C8) = C42.2Q8φ: C4⋊C8/C42 → C2 ⊆ Aut C464C4.2(C4:C8)128,13
C4.3(C4⋊C8) = C16⋊1C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4.3(C4:C8)128,100
C4.4(C4⋊C8) = C16.C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4324C4.4(C4:C8)128,101
C4.5(C4⋊C8) = C16⋊3C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4.5(C4:C8)128,103
C4.6(C4⋊C8) = C16⋊4C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4.6(C4:C8)128,104
C4.7(C4⋊C8) = C16.3C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4322C4.7(C4:C8)128,105
C4.8(C4⋊C8) = C42.2C8φ: C4⋊C8/C42 → C2 ⊆ Aut C432C4.8(C4:C8)128,107
C4.9(C4⋊C8) = M5(2)⋊C4φ: C4⋊C8/C42 → C2 ⊆ Aut C464C4.9(C4:C8)128,109
C4.10(C4⋊C8) = C2×C8⋊2C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4.10(C4:C8)128,294
C4.11(C4⋊C8) = C2×C8⋊1C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4.11(C4:C8)128,295
C4.12(C4⋊C8) = C42⋊8C8φ: C4⋊C8/C42 → C2 ⊆ Aut C4128C4.12(C4:C8)128,563
C4.13(C4⋊C8) = C4⋊M5(2)φ: C4⋊C8/C42 → C2 ⊆ Aut C464C4.13(C4:C8)128,882
C4.14(C4⋊C8) = C42.46Q8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C4128C4.14(C4:C8)128,11
C4.15(C4⋊C8) = C42.3Q8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C464C4.15(C4:C8)128,15
C4.16(C4⋊C8) = M4(2).C8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C4324C4.16(C4:C8)128,110
C4.17(C4⋊C8) = M5(2)⋊7C4φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C464C4.17(C4:C8)128,111
C4.18(C4⋊C8) = M4(2)⋊1C8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C464C4.18(C4:C8)128,297
C4.19(C4⋊C8) = C4⋊C4.7C8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C464C4.19(C4:C8)128,883
C4.20(C4⋊C8) = M4(2).1C8φ: C4⋊C8/C2×C8 → C2 ⊆ Aut C4324C4.20(C4:C8)128,885
C4.21(C4⋊C8) = C2.C82central extension (φ=1)128C4.21(C4:C8)128,5
C4.22(C4⋊C8) = C42⋊6C8central extension (φ=1)32C4.22(C4:C8)128,8
C4.23(C4⋊C8) = C22.7M5(2)central extension (φ=1)128C4.23(C4:C8)128,106
C4.24(C4⋊C8) = C42.7C8central extension (φ=1)32C4.24(C4:C8)128,108
C4.25(C4⋊C8) = C4⋊C32central extension (φ=1)128C4.25(C4:C8)128,153
C4.26(C4⋊C8) = C8.C16central extension (φ=1)322C4.26(C4:C8)128,154
C4.27(C4⋊C8) = C42.42Q8central extension (φ=1)64C4.27(C4:C8)128,296
C4.28(C4⋊C8) = C2×C4⋊C16central extension (φ=1)128C4.28(C4:C8)128,881
C4.29(C4⋊C8) = C2×C8.C8central extension (φ=1)32C4.29(C4:C8)128,884

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁