Finite Group DatabasebetaFinite Group Databasebeta| order | 24794 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C49⋊AGL(1,𝔽23) |
| unambiguous semidirect product | (C23⋊C11)⋊D49 |
| unambiguous semidirect product | D1127⋊C11 |
| Fitting, derived, Hall | C23×C49 ⋊ C2×C11 |
| Hall | C49×C23⋊C11 ⋊ C2 |
| Hall | D1127 ⋊ C11 |
| Hall | C23⋊C11 ⋊ D49 |
| Sylow | C49 ⋊ AGL(1,𝔽23) |
| Sylow | C23 ⋊ C11×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C23×C49 | C2×C11 |
| Frattini | C7 | C7⋊AGL(1,𝔽23) |
| socle | C7×C23 | C11×D7 |
| LCS | G ▷ C23×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1127 |
Polycyclic presentation:
2,7,11,23,7|b^7=e^6,b^a=b^6e,d^a=d^22,e^a=e^6,d^c=d^2335 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24794, 12);