Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(ΓL(1,𝔽8)⋊(C7⋊#261)) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊(C3⋊(C7⋊#261)) |
| Fitting, socle, derived | C3×C72×C13 ⋊ C3×C4 |
| Hall | C3×C7×C13×ΓL(1,𝔽8) ⋊ C4 |
| Hall | C72×C13 ⋊ C3×Dic3 |
| Hall | C3×C7×ΓL(1,𝔽8) ⋊ #261 |
| Sylow | C72 ⋊ C3×C3⋊#261 |
| Sylow | C13 ⋊ C3⋊(ΓL(1,𝔽8)⋊Dic7) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C72×C13 | C3×C4 |
| prime radical | C3×C7×ΓL(1,𝔽8)×D13 | C2 |
| cosocle | C3×C72×D13 | C2×C3 |
| LCS | G ▷ C3×C72×C13 | |
| UCS | C1 | |
136 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 819 |
Polycyclic presentation:
2,3,2,3,7^2,13|a^2=c,d^a=d^2,e^a=e^6,f^a=f^6,g^a=g^5,e^b=e^2,g^c=g^12429 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1128);