Finite Group DatabasebetaFinite Group Databasebeta| order | 23885 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C281⋊C5 |
| unambiguous semidirect product | C281⋊(C5×C17) |
| unambiguous semidirect product | (C17×C281)⋊C5 |
| Fitting, socle, Hall | C17×C281 ⋊ C5 |
| derived, Sylow | C281 ⋊ C5×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C281⋊C5 |
| commutator, cosocle, hypocenter | C281 | C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C17×C281 | C5 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C17 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4777 |
1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23885, 1);