Finite Group DatabasebetaFinite Group Databasebeta| order | 23780 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #18011700⋊C5 |
| Fitting, socle, derived, Hall | C29×C41 ⋊ C4×C5 |
| Hall | C29×C41⋊C5 ⋊ C4 |
| Hall | #18011700 ⋊ C5 |
| Hall | C41⋊C5 ⋊ #1181 |
| Sylow | C41 ⋊ C5×#1181 |
| Sylow | C29 ⋊ #4223⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C41 | C4×C5 |
| prime radical | C29⋊(D41⋊C5) | C2 |
| cosocle | D1189 | C2×C5 |
| LCS | G ▷ C29×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1189 |
Polycyclic presentation:
2,5,2,29,41|a^2=c,d^a=d^17,e^a=e^32,e^b=e^10,d^c=d^28,e^c=e^40113 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23780, 15);