Finite Group DatabasebetaFinite Group Databasebeta| order | 23180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C19⋊#11927414 |
| Fitting, socle, derived, Hall | C5×C19×C61 ⋊ C4 |
| Hall | C19×C61 ⋊ AGL(1,𝔽5) |
| Hall | C5×C61 ⋊ Dic19 |
| Hall | C5×C19 ⋊ Dic61 |
| Sylow | C61 ⋊ C19⋊AGL(1,𝔽5) |
| Sylow | C19 ⋊ #11927414 |
| Sylow | C5 ⋊ Dic1159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C19×C61 | C4 |
| prime radical, cosocle | D5×C19×C61 | 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^2,d^a=d^18,e^a=e^60,c^b=c^42321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23180, 31);