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

Extensions 1→N→G→Q→1 with N=Q8×C32 and Q=S3

Direct product G=N×Q with N=Q8×C32 and Q=S3
dρLabelID
S3×Q8×C32144S3xQ8xC3^2432,706

Semidirect products G=N:Q with N=Q8×C32 and Q=S3
extensionφ:Q→Out NdρLabelID
(Q8×C32)⋊1S3 = He3⋊10SD16φ: S3/C1 → S3 ⊆ Out Q8×C327212+(Q8xC3^2):1S3432,161
(Q8×C32)⋊2S3 = He3⋊11SD16φ: S3/C1 → S3 ⊆ Out Q8×C32726(Q8xC3^2):2S3432,196
(Q8×C32)⋊3S3 = C32⋊2GL2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C327212+(Q8xC3^2):3S3432,248
(Q8×C32)⋊4S3 = C32⋊3GL2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C32726(Q8xC3^2):4S3432,258
(Q8×C32)⋊5S3 = Q8×C32⋊C6φ: S3/C1 → S3 ⊆ Out Q8×C327212-(Q8xC3^2):5S3432,368
(Q8×C32)⋊6S3 = (Q8×He3)⋊C2φ: S3/C1 → S3 ⊆ Out Q8×C327212+(Q8xC3^2):6S3432,369
(Q8×C32)⋊7S3 = Q8×He3⋊C2φ: S3/C1 → S3 ⊆ Out Q8×C32726(Q8xC3^2):7S3432,394
(Q8×C32)⋊8S3 = He3⋊5D4⋊C2φ: S3/C1 → S3 ⊆ Out Q8×C32726(Q8xC3^2):8S3432,395
(Q8×C32)⋊9S3 = C3×C6.6S4φ: S3/C1 → S3 ⊆ Out Q8×C32484(Q8xC3^2):9S3432,617
(Q8×C32)⋊10S3 = C32⋊5GL2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C3272(Q8xC3^2):10S3432,620
(Q8×C32)⋊11S3 = C32×GL2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C3272(Q8xC3^2):11S3432,614
(Q8×C32)⋊12S3 = C3×C32⋊11SD16φ: S3/C3 → C2 ⊆ Out Q8×C32144(Q8xC3^2):12S3432,493
(Q8×C32)⋊13S3 = C33⋊27SD16φ: S3/C3 → C2 ⊆ Out Q8×C32216(Q8xC3^2):13S3432,509
(Q8×C32)⋊14S3 = C3×Q8×C3⋊S3φ: S3/C3 → C2 ⊆ Out Q8×C32144(Q8xC3^2):14S3432,716
(Q8×C32)⋊15S3 = C3×C12.26D6φ: S3/C3 → C2 ⊆ Out Q8×C32144(Q8xC3^2):15S3432,717
(Q8×C32)⋊16S3 = Q8×C33⋊C2φ: S3/C3 → C2 ⊆ Out Q8×C32216(Q8xC3^2):16S3432,726
(Q8×C32)⋊17S3 = (Q8×C33)⋊C2φ: S3/C3 → C2 ⊆ Out Q8×C32216(Q8xC3^2):17S3432,727
(Q8×C32)⋊18S3 = C32×Q8⋊2S3φ: S3/C3 → C2 ⊆ Out Q8×C32144(Q8xC3^2):18S3432,477
(Q8×C32)⋊19S3 = C32×Q8⋊3S3φ: trivial image144(Q8xC3^2):19S3432,707

Non-split extensions G=N.Q with N=Q8×C32 and Q=S3
extensionφ:Q→Out NdρLabelID
(Q8×C32).1S3 = He3⋊6Q16φ: S3/C1 → S3 ⊆ Out Q8×C3214412-(Q8xC3^2).1S3432,160
(Q8×C32).2S3 = Dic18.C6φ: S3/C1 → S3 ⊆ Out Q8×C3214412-(Q8xC3^2).2S3432,162
(Q8×C32).3S3 = D36.C6φ: S3/C1 → S3 ⊆ Out Q8×C327212+(Q8xC3^2).3S3432,163
(Q8×C32).4S3 = He3⋊7Q16φ: S3/C1 → S3 ⊆ Out Q8×C321446(Q8xC3^2).4S3432,197
(Q8×C32).5S3 = C32.CSU2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C3214412-(Q8xC3^2).5S3432,243
(Q8×C32).6S3 = C3×Q8.D9φ: S3/C1 → S3 ⊆ Out Q8×C321444(Q8xC3^2).6S3432,244
(Q8×C32).7S3 = C32.GL2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C327212+(Q8xC3^2).7S3432,245
(Q8×C32).8S3 = C3×Q8⋊D9φ: S3/C1 → S3 ⊆ Out Q8×C321444(Q8xC3^2).8S3432,246
(Q8×C32).9S3 = C32⋊CSU2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C3214412-(Q8xC3^2).9S3432,247
(Q8×C32).10S3 = C32.3CSU2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C32432(Q8xC3^2).10S3432,255
(Q8×C32).11S3 = C32.3GL2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C32216(Q8xC3^2).11S3432,256
(Q8×C32).12S3 = C32⋊2CSU2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C321446(Q8xC3^2).12S3432,257
(Q8×C32).13S3 = Q8×C9⋊C6φ: S3/C1 → S3 ⊆ Out Q8×C327212-(Q8xC3^2).13S3432,370
(Q8×C32).14S3 = D36⋊3C6φ: S3/C1 → S3 ⊆ Out Q8×C327212+(Q8xC3^2).14S3432,371
(Q8×C32).15S3 = C3×C6.5S4φ: S3/C1 → S3 ⊆ Out Q8×C32484(Q8xC3^2).15S3432,616
(Q8×C32).16S3 = C32⋊4CSU2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C32144(Q8xC3^2).16S3432,619
(Q8×C32).17S3 = C32×CSU2(𝔽3)φ: S3/C1 → S3 ⊆ Out Q8×C32144(Q8xC3^2).17S3432,613
(Q8×C32).18S3 = C3×C9⋊Q16φ: S3/C3 → C2 ⊆ Out Q8×C321444(Q8xC3^2).18S3432,156
(Q8×C32).19S3 = C3×Q8⋊2D9φ: S3/C3 → C2 ⊆ Out Q8×C321444(Q8xC3^2).19S3432,157
(Q8×C32).20S3 = C36.19D6φ: S3/C3 → C2 ⊆ Out Q8×C32432(Q8xC3^2).20S3432,194
(Q8×C32).21S3 = C36.20D6φ: S3/C3 → C2 ⊆ Out Q8×C32216(Q8xC3^2).21S3432,195
(Q8×C32).22S3 = C3×Q8×D9φ: S3/C3 → C2 ⊆ Out Q8×C321444(Q8xC3^2).22S3432,364
(Q8×C32).23S3 = C3×Q8⋊3D9φ: S3/C3 → C2 ⊆ Out Q8×C321444(Q8xC3^2).23S3432,365
(Q8×C32).24S3 = Q8×C9⋊S3φ: S3/C3 → C2 ⊆ Out Q8×C32216(Q8xC3^2).24S3432,392
(Q8×C32).25S3 = C36.29D6φ: S3/C3 → C2 ⊆ Out Q8×C32216(Q8xC3^2).25S3432,393
(Q8×C32).26S3 = C3×C32⋊7Q16φ: S3/C3 → C2 ⊆ Out Q8×C32144(Q8xC3^2).26S3432,494
(Q8×C32).27S3 = C33⋊15Q16φ: S3/C3 → C2 ⊆ Out Q8×C32432(Q8xC3^2).27S3432,510
(Q8×C32).28S3 = C32×C3⋊Q16φ: S3/C3 → C2 ⊆ Out Q8×C32144(Q8xC3^2).28S3432,478

׿
×
⋊
ℤ
𝔽
○
≀
ℚ
◁