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

Extensions 1→N→G→Q→1 with N=C10 and Q=C5⋊D4

Direct product G=N×Q with N=C10 and Q=C5⋊D4
dρLabelID
C10×C5⋊D440C10xC5:D4400,190

Semidirect products G=N:Q with N=C10 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C10⋊1(C5⋊D4) = C2×C5⋊D20φ: C5⋊D4/Dic5 → C2 ⊆ Aut C1040C10:1(C5:D4)400,177
C10⋊2(C5⋊D4) = C2×C52⋊2D4φ: C5⋊D4/D10 → C2 ⊆ Aut C1080C10:2(C5:D4)400,176
C10⋊3(C5⋊D4) = C2×C52⋊7D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10:3(C5:D4)400,200

Non-split extensions G=N.Q with N=C10 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C10.1(C5⋊D4) = C5⋊D40φ: C5⋊D4/Dic5 → C2 ⊆ Aut C10404+C10.1(C5:D4)400,65
C10.2(C5⋊D4) = C52⋊3SD16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C10804-C10.2(C5:D4)400,67
C10.3(C5⋊D4) = C52⋊4SD16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C10404+C10.3(C5:D4)400,68
C10.4(C5⋊D4) = C52⋊3Q16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C10804-C10.4(C5:D4)400,70
C10.5(C5⋊D4) = C10.D20φ: C5⋊D4/Dic5 → C2 ⊆ Aut C1040C10.5(C5:D4)400,73
C10.6(C5⋊D4) = Dic5⋊Dic5φ: C5⋊D4/Dic5 → C2 ⊆ Aut C1080C10.6(C5:D4)400,74
C10.7(C5⋊D4) = C52⋊2D8φ: C5⋊D4/D10 → C2 ⊆ Aut C10804C10.7(C5:D4)400,64
C10.8(C5⋊D4) = D20.D5φ: C5⋊D4/D10 → C2 ⊆ Aut C10804C10.8(C5:D4)400,66
C10.9(C5⋊D4) = C52⋊2Q16φ: C5⋊D4/D10 → C2 ⊆ Aut C10804C10.9(C5:D4)400,69
C10.10(C5⋊D4) = D10⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C1080C10.10(C5:D4)400,72
C10.11(C5⋊D4) = C10.Dic10φ: C5⋊D4/D10 → C2 ⊆ Aut C1080C10.11(C5:D4)400,75
C10.12(C5⋊D4) = C50.D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10400C10.12(C5:D4)400,12
C10.13(C5⋊D4) = D50⋊C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.13(C5:D4)400,14
C10.14(C5⋊D4) = D4.D25φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C102004-C10.14(C5:D4)400,15
C10.15(C5⋊D4) = D4⋊D25φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C102004+C10.15(C5:D4)400,16
C10.16(C5⋊D4) = C25⋊Q16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C104004-C10.16(C5:D4)400,17
C10.17(C5⋊D4) = Q8⋊D25φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C102004+C10.17(C5:D4)400,18
C10.18(C5⋊D4) = C23.D25φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.18(C5:D4)400,19
C10.19(C5⋊D4) = C2×C25⋊D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.19(C5:D4)400,44
C10.20(C5⋊D4) = C102.22C22φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10400C10.20(C5:D4)400,100
C10.21(C5⋊D4) = C10.11D20φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.21(C5:D4)400,102
C10.22(C5⋊D4) = C52⋊7D8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.22(C5:D4)400,103
C10.23(C5⋊D4) = C52⋊8SD16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.23(C5:D4)400,104
C10.24(C5⋊D4) = C52⋊10SD16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.24(C5:D4)400,105
C10.25(C5⋊D4) = C52⋊7Q16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10400C10.25(C5:D4)400,106
C10.26(C5⋊D4) = C102⋊11C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C10200C10.26(C5:D4)400,107
C10.27(C5⋊D4) = C5×C10.D4central extension (φ=1)80C10.27(C5:D4)400,84
C10.28(C5⋊D4) = C5×D10⋊C4central extension (φ=1)80C10.28(C5:D4)400,86
C10.29(C5⋊D4) = C5×D4⋊D5central extension (φ=1)404C10.29(C5:D4)400,87
C10.30(C5⋊D4) = C5×D4.D5central extension (φ=1)404C10.30(C5:D4)400,88
C10.31(C5⋊D4) = C5×Q8⋊D5central extension (φ=1)804C10.31(C5:D4)400,89
C10.32(C5⋊D4) = C5×C5⋊Q16central extension (φ=1)804C10.32(C5:D4)400,90
C10.33(C5⋊D4) = C5×C23.D5central extension (φ=1)40C10.33(C5:D4)400,91

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁