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

Extensions 1→N→G→Q→1 with N=C10 and Q=C4⋊Q8

Direct product G=N×Q with N=C10 and Q=C4⋊Q8
dρLabelID
C10×C4⋊Q8320C10xC4:Q8320,1533

Semidirect products G=N:Q with N=C10 and Q=C4⋊Q8
extensionφ:Q→Aut NdρLabelID
C10⋊1(C4⋊Q8) = C2×C20⋊2Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10:1(C4:Q8)320,1140
C10⋊2(C4⋊Q8) = C2×C20⋊Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10:2(C4:Q8)320,1169
C10⋊3(C4⋊Q8) = C2×Dic5⋊Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10:3(C4:Q8)320,1482

Non-split extensions G=N.Q with N=C10 and Q=C4⋊Q8
extensionφ:Q→Aut NdρLabelID
C10.1(C4⋊Q8) = C10.(C4⋊Q8)φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.1(C4:Q8)320,288
C10.2(C4⋊Q8) = C40⋊9Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.2(C4:Q8)320,307
C10.3(C4⋊Q8) = C40⋊8Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.3(C4:Q8)320,309
C10.4(C4⋊Q8) = C40.13Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.4(C4:Q8)320,310
C10.5(C4⋊Q8) = C8⋊Dic10φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.5(C4:Q8)320,329
C10.6(C4⋊Q8) = C20⋊7(C4⋊C4)φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.6(C4:Q8)320,555
C10.7(C4⋊Q8) = (C2×C20)⋊10Q8φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.7(C4:Q8)320,556
C10.8(C4⋊Q8) = C42⋊8Dic5φ: C4⋊Q8/C42 → C2 ⊆ Aut C10320C10.8(C4:Q8)320,562
C10.9(C4⋊Q8) = (C2×C20)⋊Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.9(C4:Q8)320,273
C10.10(C4⋊Q8) = C10.49(C4×D4)φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.10(C4:Q8)320,274
C10.11(C4⋊Q8) = (C2×Dic5)⋊Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.11(C4:Q8)320,283
C10.12(C4⋊Q8) = C2.(C20⋊Q8)φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.12(C4:Q8)320,284
C10.13(C4⋊Q8) = C40⋊5Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.13(C4:Q8)320,482
C10.14(C4⋊Q8) = C40⋊3Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.14(C4:Q8)320,483
C10.15(C4⋊Q8) = C8.8Dic10φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.15(C4:Q8)320,485
C10.16(C4⋊Q8) = C40⋊2Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.16(C4:Q8)320,501
C10.17(C4⋊Q8) = C40⋊4Q8φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.17(C4:Q8)320,503
C10.18(C4⋊Q8) = C8.6Dic10φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.18(C4:Q8)320,505
C10.19(C4⋊Q8) = C20⋊4(C4⋊C4)φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.19(C4:Q8)320,600
C10.20(C4⋊Q8) = C20⋊5(C4⋊C4)φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.20(C4:Q8)320,603
C10.21(C4⋊Q8) = (C2×C4)⋊Dic10φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.21(C4:Q8)320,606
C10.22(C4⋊Q8) = (C2×C20).54D4φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.22(C4:Q8)320,611
C10.23(C4⋊Q8) = C20⋊6(C4⋊C4)φ: C4⋊Q8/C4⋊C4 → C2 ⊆ Aut C10320C10.23(C4:Q8)320,612
C10.24(C4⋊Q8) = C10.96(C4×D4)φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.24(C4:Q8)320,599
C10.25(C4⋊Q8) = (C2×Dic5)⋊6Q8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.25(C4:Q8)320,601
C10.26(C4⋊Q8) = (C2×C20).287D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.26(C4:Q8)320,607
C10.27(C4⋊Q8) = (C2×C20).53D4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.27(C4:Q8)320,610
C10.28(C4⋊Q8) = C42.215D10φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.28(C4:Q8)320,691
C10.29(C4⋊Q8) = C42.68D10φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.29(C4:Q8)320,692
C10.30(C4⋊Q8) = C20.17D8φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.30(C4:Q8)320,705
C10.31(C4⋊Q8) = C20.SD16φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.31(C4:Q8)320,706
C10.32(C4⋊Q8) = C42.76D10φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.32(C4:Q8)320,707
C10.33(C4⋊Q8) = C10.C22≀C2φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.33(C4:Q8)320,856
C10.34(C4⋊Q8) = (Q8×C10)⋊17C4φ: C4⋊Q8/C2×Q8 → C2 ⊆ Aut C10320C10.34(C4:Q8)320,857
C10.35(C4⋊Q8) = C5×C42⋊9C4central extension (φ=1)320C10.35(C4:Q8)320,885
C10.36(C4⋊Q8) = C5×C23.65C23central extension (φ=1)320C10.36(C4:Q8)320,890
C10.37(C4⋊Q8) = C5×C23.67C23central extension (φ=1)320C10.37(C4:Q8)320,892
C10.38(C4⋊Q8) = C5×C23.78C23central extension (φ=1)320C10.38(C4:Q8)320,896
C10.39(C4⋊Q8) = C5×C23.81C23central extension (φ=1)320C10.39(C4:Q8)320,899
C10.40(C4⋊Q8) = C5×C8⋊3Q8central extension (φ=1)320C10.40(C4:Q8)320,999
C10.41(C4⋊Q8) = C5×C8.5Q8central extension (φ=1)320C10.41(C4:Q8)320,1000
C10.42(C4⋊Q8) = C5×C8⋊2Q8central extension (φ=1)320C10.42(C4:Q8)320,1001
C10.43(C4⋊Q8) = C5×C8⋊Q8central extension (φ=1)320C10.43(C4:Q8)320,1002

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁