Finite Group DatabasebetaFinite Group Databasebeta| order | 22932 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C3×C7×PSL(2,𝔽13) |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3×C7 | PSL(2,𝔽13) |
| commutator, hypocenter | PSL(2,𝔽13) | C3×C7 |
| Frattini | C1 | G |
| LCS | G ▷ PSL(2,𝔽13) | |
| UCS | C1 ◁ C3×C7 | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 294 |
A minimal faithful permutation representation — 2 generators on 24 points:
(12,13,20)(14,21,24)(15,16,18)(17,22,23);(1,2,3)(4,5,6,7,8,9,10)(11,12)(13,15)(14,16)(18,22)(19,23)(21,24)189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22932, 1631);