Finite Group DatabasebetaFinite Group Databasebeta| order | 24255 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3×C7 |
| direct product | C3×C11⋊C5×#3862 |
| unambiguous semidirect product | C11⋊(C3×C5×#3862) |
| unambiguous semidirect product | (C3×C11)⋊(C5×#3862) |
| unambiguous semidirect product | (C3×C11×#3862)⋊C5 |
| Fitting, socle | C3×C72×C11 ⋊ C3×C5 |
| derived, Hall | C72×C11 ⋊ C32×C5 |
| Hall | C3×C11×#3862 ⋊ C5 |
| Hall | C72×C11⋊C5 ⋊ C32 |
| Sylow | C72 ⋊ C32×C11⋊C5 |
| Sylow | C11 ⋊ C3×C5×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C11⋊C5×#3862 |
| commutator, cosocle, hypocenter | C72×C11 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C11 | C3×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 ◁ C3 | |
112 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, 21);