Finite Group DatabasebetaFinite Group Databasebeta| order | 31515 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#24901882 |
| Fitting, socle, Hall | C3×C11×C191 ⋊ C5 |
| derived, Hall | C11×C191 ⋊ C3×C5 |
| Hall | C3×C191 ⋊ C11⋊C5 |
| Sylow | C191 ⋊ C3×C11⋊C5 |
| Hall | C3×C11 ⋊ C191⋊C5 |
| Sylow | C11 ⋊ C3×C191⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #24901882 |
| commutator, cosocle, hypocenter | C11×C191 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C11×C191 | C5 |
| LCS | G ▷ C11×C191 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6303 |
1275 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31515, 6);