Finite Group DatabasebetaFinite Group Databasebeta| order | 30195 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| direct product | C3×#16809822⋊C3 |
| unambiguous semidirect product | #16809822⋊C32 |
| unambiguous semidirect product | (C3×#16809822)⋊C3 |
| Fitting, socle | C3×C11×C61 ⋊ C3×C5 |
| derived, Hall | C11×C61 ⋊ C32×C5 |
| Hall | C3×C11×C61⋊C3 ⋊ C5 |
| Hall | #16809822 ⋊ C32 |
| Hall | C3×C61⋊C3 ⋊ C11⋊C5 |
| Sylow | C61 ⋊ C32×C11⋊C5 |
| Sylow | C11 ⋊ C3×(C61⋊C3)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16809822⋊C3 |
| commutator, cosocle, hypocenter | C11×C61 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C61 | C3×C5 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2013 |
195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30195, 20);