Finite Group DatabasebetaFinite Group Databasebeta| order | 15345 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#13133724 |
| Fitting, Hall | C9×C11×C31 ⋊ C5 |
| derived, Hall | C11×C31 ⋊ C5×C9 |
| Hall | C9×C31 ⋊ C11⋊C5 |
| Hall | C9×C11 ⋊ ΓL(1,𝔽32) |
| Sylow | C31 ⋊ C9×C11⋊C5 |
| Sylow | C11 ⋊ C9×ΓL(1,𝔽32) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #13133724 |
| commutator, hypocenter | C11×C31 | C5×C9 |
| Frattini | C3 | C3×#13133724 |
| Fitting | C9×C11×C31 | C5 |
| socle, cosocle | C3×C11×C31 | C3×C5 |
| prime radical | C3×#13133724 | C3 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3069 |
657 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×#13133724, C9×#16811774, C9×#16811780, … |
| maximal normal subgroup of | C2×C9×#13133724, C9×#16811774, C9×#16811780, … |
| maximal quotient of | C2×C9×#13133724 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15345, 7);