Finite Group DatabasebetaFinite Group Databasebeta| order | 24475 |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C11 · Schur multiplier (H2) = C5 |
| direct product | C52×C89⋊C11 |
| unambiguous semidirect product | C89⋊(C52×C11) |
| unambiguous semidirect product | (C5×C89)⋊(C5×C11) |
| unambiguous semidirect product | (C52×C89)⋊C11 |
| Fitting, socle, Hall | C52×C89 ⋊ C11 |
| derived, Sylow | C89 ⋊ C52×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C89⋊C11 |
| commutator, cosocle, hypocenter | C89 | C52×C11 |
| Frattini | C1 | G |
| Fitting, socle | C52×C89 | C11 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2225 |
475 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24475, 5);