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

Extensions 1→N→G→Q→1 with N=C4 and Q=C15⋊D4

Direct product G=N×Q with N=C4 and Q=C15⋊D4
dρLabelID
C4×C15⋊D4240C4xC15:D4480,515

Semidirect products G=N:Q with N=C4 and Q=C15⋊D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C15⋊D4) = C60⋊10D4φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4240C4:1(C15:D4)480,539
C4⋊2(C15⋊D4) = C60⋊D4φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C4240C4:2(C15:D4)480,525
C4⋊3(C15⋊D4) = C60⋊4D4φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C4240C4:3(C15:D4)480,532

Non-split extensions G=N.Q with N=C4 and Q=C15⋊D4
extensionφ:Q→Aut NdρLabelID
C4.1(C15⋊D4) = C15⋊D16φ: C15⋊D4/Dic15 → C2 ⊆ Aut C42404C4.1(C15:D4)480,13
C4.2(C15⋊D4) = C40.D6φ: C15⋊D4/Dic15 → C2 ⊆ Aut C42404C4.2(C15:D4)480,16
C4.3(C15⋊D4) = C15⋊SD32φ: C15⋊D4/Dic15 → C2 ⊆ Aut C42404C4.3(C15:D4)480,17
C4.4(C15⋊D4) = C15⋊Q32φ: C15⋊D4/Dic15 → C2 ⊆ Aut C44804C4.4(C15:D4)480,22
C4.5(C15⋊D4) = C2×C15⋊D8φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4240C4.5(C15:D4)480,372
C4.6(C15⋊D4) = C2×C30.D4φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4240C4.6(C15:D4)480,382
C4.7(C15⋊D4) = C2×C20.D6φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4240C4.7(C15:D4)480,384
C4.8(C15⋊D4) = C2×C15⋊Q16φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4480C4.8(C15:D4)480,394
C4.9(C15⋊D4) = C60.88D4φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4240C4.9(C15:D4)480,444
C4.10(C15⋊D4) = C60.89D4φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4240C4.10(C15:D4)480,446
C4.11(C15⋊D4) = Dic15⋊8Q8φ: C15⋊D4/Dic15 → C2 ⊆ Aut C4480C4.11(C15:D4)480,461
C4.12(C15⋊D4) = C20.5D12φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C41204C4.12(C15:D4)480,35
C4.13(C15⋊D4) = C60.54D4φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C42404C4.13(C15:D4)480,38
C4.14(C15⋊D4) = C10.D24φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C4240C4.14(C15:D4)480,43
C4.15(C15⋊D4) = C10.Dic12φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C4480C4.15(C15:D4)480,49
C4.16(C15⋊D4) = D20⋊21D6φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C41204C4.16(C15:D4)480,375
C4.17(C15⋊D4) = D20.37D6φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C42404C4.17(C15:D4)480,383
C4.18(C15⋊D4) = C60.67D4φ: C15⋊D4/C6×D5 → C2 ⊆ Aut C4240C4.18(C15:D4)480,435
C4.19(C15⋊D4) = C60.28D4φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C41204C4.19(C15:D4)480,34
C4.20(C15⋊D4) = C12.6D20φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C42404C4.20(C15:D4)480,37
C4.21(C15⋊D4) = C6.D40φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C4240C4.21(C15:D4)480,41
C4.22(C15⋊D4) = C6.Dic20φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C4480C4.22(C15:D4)480,47
C4.23(C15⋊D4) = C60.36D4φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C41204C4.23(C15:D4)480,374
C4.24(C15⋊D4) = D12.37D10φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C42404C4.24(C15:D4)480,385
C4.25(C15⋊D4) = C60.46D4φ: C15⋊D4/S3×C10 → C2 ⊆ Aut C4240C4.25(C15:D4)480,445
C4.26(C15⋊D4) = C60.93D4central extension (φ=1)240C4.26(C15:D4)480,31
C4.27(C15⋊D4) = C60.94D4central extension (φ=1)240C4.27(C15:D4)480,32
C4.28(C15⋊D4) = C60.96D4central extension (φ=1)1204C4.28(C15:D4)480,52
C4.29(C15⋊D4) = C60.98D4central extension (φ=1)1204C4.29(C15:D4)480,54
C4.30(C15⋊D4) = C60.14Q8central extension (φ=1)480C4.30(C15:D4)480,59
C4.31(C15⋊D4) = C60.D4central extension (φ=1)2404C4.31(C15:D4)480,68
C4.32(C15⋊D4) = D20.34D6central extension (φ=1)2404C4.32(C15:D4)480,373

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁