Finite Group DatabasebetaFinite Group Databasebeta| order | 15345 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13133721⋊C9 |
| derived, Hall | C11×C31 ⋊ C5×C9 |
| Hall | C11×C31⋊C9 ⋊ C5 |
| Hall | #13133721 ⋊ C9 |
| Hall | C31⋊C9 ⋊ C11⋊C5 |
| Sylow | C31 ⋊ C9×C11⋊C5 |
| Sylow | C11 ⋊ ΓL(1,𝔽32)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #13133721⋊C3 |
| commutator, hypocenter | C11×C31 | C5×C9 |
| Fitting, socle, cosocle | C3×C11×C31 | C3×C5 |
| prime radical | C3×#13133721 | C3 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
Polycyclic presentation:
3,5,11,31,3|a^3=e,d^a=d^25,c^b=c^4,d^b=d^16129 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#13133721⋊C9, #16811771⋊C9, #16811777⋊C9, … |
| maximal normal subgroup of | C2×#13133721⋊C9, #16811771⋊C9, #16811777⋊C9, … |
| maximal quotient of | C2×#13133721⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15345, 11);