Finite Group DatabasebetaFinite Group Databasebeta| order | 23045 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C419 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×C419 |
| unambiguous semidirect product | C11⋊(C5×C419) |
| unambiguous semidirect product | (C11×C419)⋊C5 |
| Fitting, socle, Hall | C11×C419 ⋊ C5 |
| derived, Sylow | C11 ⋊ C5×C419 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C419 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C5×C419 |
| Frattini | C1 | G |
| Fitting, socle | C11×C419 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C419 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4609 |
2933 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23045, 2);