Finite Group DatabasebetaFinite Group Databasebeta| order | 30195 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#16809824 |
| Fitting, Hall | C9×C11×C61 ⋊ C5 |
| derived, Hall | C11×C61 ⋊ C5×C9 |
| Hall | C9×C61 ⋊ C11⋊C5 |
| Hall | C9×C11 ⋊ C61⋊C5 |
| Sylow | C61 ⋊ C9×C11⋊C5 |
| Sylow | C11 ⋊ C9×C61⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #16809824 |
| commutator, hypocenter | C11×C61 | C5×C9 |
| Frattini | C3 | C3×#16809824 |
| Fitting | C9×C11×C61 | C5 |
| socle, cosocle | C3×C11×C61 | C3×C5 |
| prime radical | C3×#16809824 | C3 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
1251 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30195, 4);