Finite Group DatabasebetaFinite Group Databasebeta| order | 24255 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C7 |
| direct product | C11⋊C5×#89205 |
| unambiguous semidirect product | C11⋊(C5×#89205) |
| unambiguous semidirect product | (C11×#89205)⋊C5 |
| derived, Hall | C72×C11 ⋊ C5×C9 |
| Hall | C11×#89205 ⋊ C5 |
| Hall | C72×C11⋊C5 ⋊ C9 |
| Sylow | C72 ⋊ C9×C11⋊C5 |
| Sylow | C11 ⋊ C5×#89205 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C11⋊C5×#3862 |
| commutator, hypocenter | C72×C11 | C5×C9 |
| Fitting, socle, cosocle | C3×C72×C11 | C3×C5 |
| prime radical | C3×C72×C11⋊C5 | C3 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 693 |
399 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24255, 12);