Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#11927415 |
| Fitting, socle, derived, Hall | C5×C19×C61 ⋊ C4 |
| Hall | C19×C61 ⋊ Dic5 |
| Hall | C5×C61 ⋊ Dic19 |
| Hall | C5×C19 ⋊ #6923 |
| Sylow | C61 ⋊ Dic95 |
| Sylow | C19 ⋊ #11927415 |
| Sylow | C5 ⋊ C19⋊#6923 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C61 | C4 |
| prime radical, cosocle | C5×C19×D61 | C2 |
| LCS | G ▷ C5×C19×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5795 |
Polycyclic presentation:
2^2,5,19,61|a^2=b,c^a=c^4,d^a=d^18,e^a=e^50,e^b=e^601523 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 34);