Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D95⋊D61 |
| unambiguous semidirect product | D305⋊D19 |
| unambiguous semidirect product | D1159⋊D5 |
| Fitting, socle, derived, Hall | C5×C19×C61 ⋊ C22 |
| Hall | C19×C61 ⋊ C2×D5 |
| Hall | C5×C61 ⋊ C2×D19 |
| Hall | C5×C19 ⋊ C2×D61 |
| Sylow | C61 ⋊ D5×D19 |
| Sylow | C19 ⋊ D5×D61 |
| Sylow | C5 ⋊ D19×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C19×C61 | C22 |
| LCS | G ▷ C5×C19×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5795 |
Polycyclic presentation:
2^2,5,19,61|d^a=d^18,e^a=e^60,c^b=c^4,d^b=d^181514 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 39);