Finite Group DatabasebetaFinite Group Databasebeta| order | 23580 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| derived, Hall | C22×C131 ⋊ C5×C9 |
| Hall | C22⋊C9×C131 ⋊ C5 |
| Hall | C22×C131⋊C5 ⋊ C9 |
| Sylow | C131 ⋊ C5×C22⋊C9 |
| Sylow | C22 ⋊ C9×C131⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×C131⋊C5 |
| commutator, hypocenter | C22×C131 | C5×C9 |
| Fitting, socle, cosocle | C22×C3×C131 | C3×C5 |
| prime radical | C22×C3×C131⋊C5 | C3 |
| LCS | G ▷ C22×C131 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2358 |
372 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23580, 15);