Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C5×C19×#6923 |
| Fitting, socle, Hall | C5×C19×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C4×C5×C19 |
| Hall | C19×C61 ⋊ C4×C5 |
| Hall | C5×C61 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C19 | #6923 |
| commutator, hypocenter | C61 | C4×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C61 | C4 |
| prime radical | C5×C19×D61 | C2 |
| cosocle | D61 | C2×C5×C19 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C5×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5795 |
1805 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 21);