Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic305 |
| derived, Hall | C5×C61 ⋊ C4×C19 |
| Hall | C5×C19×C61 ⋊ C4 |
| Hall | C19×C61 ⋊ Dic5 |
| Hall | C5×C19 ⋊ Dic61 |
| Sylow | C61 ⋊ C19×Dic5 |
| Sylow | C5 ⋊ C19×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D305 |
| commutator, hypocenter | C5×C61 | C4×C19 |
| Frattini | C2 | C19×D305 |
| Fitting, socle, prime radical | C2×C5×C19×C61 | C2 |
| cosocle | C2×C5×C61 | C2×C19 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C2×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23180 |
5852 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 7);