Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊(C7⋊#261) |
| derived, Hall | C72×C13 ⋊ C4×C9 |
| Hall | C7×C13×C7⋊C9 ⋊ C4 |
| Hall | C7⋊(C7⋊#261) ⋊ C9 |
| Hall | C7×C7⋊C9 ⋊ #261 |
| Sylow | C72 ⋊ C9×#261 |
| Sylow | C13 ⋊ (C7⋊C9)⋊Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊(C7⋊#261) |
| commutator, hypocenter | C72×C13 | C4×C9 |
| Fitting, socle | C3×C72×C13 | C3×C4 |
| prime radical, cosocle | C3×C72×D13 | C2×C3 |
| LCS | G ▷ C72×C13 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 819 |
Polycyclic presentation:
2,3,2,7^2,13,3|a^2=c,b^3=g,d^a=d^6,e^a=e^6,f^a=f^5,d^b=d^2,f^c=f^12447 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 411);