Finite Group DatabasebetaFinite Group Databasebeta| order | 23780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C29 · Schur multiplier (H2) = C2 |
| direct product | C22×C29×C41⋊C5 |
| unambiguous semidirect product | (C22×C41)⋊(C5×C29) |
| unambiguous semidirect product | (C22×C29×C41)⋊C5 |
| Fitting, socle, Hall | C22×C29×C41 ⋊ C5 |
| derived, Sylow | C41 ⋊ C22×C5×C29 |
| Hall | C29×C41 ⋊ C22×C5 |
| Hall | C22×C41 ⋊ C5×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C29 | C41⋊C5 |
| commutator, cosocle, hypocenter | C41 | C22×C5×C29 |
| Frattini | C1 | G |
| Fitting, socle | C22×C29×C41 | C5 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C22×C29 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4756 |
1508 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23780, 24);