Finite Group DatabasebetaFinite Group Databasebeta| order | 23780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | #1181×C41⋊C5 |
| unambiguous semidirect product | (C41×#1181)⋊C5 |
| Fitting, socle, derived, Hall | C29×C41 ⋊ C4×C5 |
| Hall | C29×C41⋊C5 ⋊ C4 |
| Hall | C41×#1181 ⋊ C5 |
| Sylow | C41 ⋊ C5×#1181 |
| Sylow | C29 ⋊ C4×C41⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C41 | C4×C5 |
| prime radical | D29×C41⋊C5 | C2 |
| cosocle | C41×D29 | C2×C5 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1189 |
143 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23780, 18);