Finite Group DatabasebetaFinite Group Databasebeta| order | 23780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C29×C41 ⋊ C22×C5 |
| Hall | C29×C41⋊C5 ⋊ C22 |
| Hall | D29×D41 ⋊ C5 |
| Hall | C41⋊C5 ⋊ C2×D29 |
| Sylow | C41 ⋊ C2×C5×D29 |
| Sylow | C29 ⋊ C2×D41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C29×C41 | C22×C5 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1189 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23780, 20);