Finite Group DatabasebetaFinite Group Databasebeta| order | 31790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1 |
| Fitting, socle, Hall | C11×C172 ⋊ C2×C5 |
| derived | C11×C17 ⋊ C2×C5×C17 |
| Hall | C172×C11⋊C5 ⋊ C2 |
| Hall | C17×D187 ⋊ C5 |
| Sylow | C172 ⋊ AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ C17×D17 |
| Sylow | C11 ⋊ C5×C17×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C17⋊AGL(1,𝔽11) |
| commutator, cosocle, hypocenter | C11×C17 | C2×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C11×C172 | C2×C5 |
| LCS | G ▷ C11×C17 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 374 |
1139 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31790, 15);