Finite Group DatabasebetaFinite Group Databasebeta| order | 30195 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16809823⋊C9 |
| derived, Hall | C11×C61 ⋊ C5×C9 |
| Hall | C11×C61⋊C9 ⋊ C5 |
| Hall | #16809823 ⋊ C9 |
| Hall | C61⋊C9 ⋊ C11⋊C5 |
| Sylow | C61 ⋊ C9×C11⋊C5 |
| Sylow | C11 ⋊ (C61⋊C5)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #16809823⋊C3 |
| commutator, hypocenter | C11×C61 | C5×C9 |
| Fitting, socle, cosocle | C3×C11×C61 | C3×C5 |
| prime radical | C3×#16809823 | C3 |
| LCS | G ▷ C11×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
Polycyclic presentation:
3,5,11,61,3|a^3=e,d^a=d^47,c^b=c^4,d^b=d^58195 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30195, 13);