Finite Group DatabasebetaFinite Group Databasebeta| order | 11781 |
| isoclinism | isoclinic class of ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C11×C17 · Schur multiplier (H2) = C1 |
| derived, Sylow | C7 ⋊ C9×C11×C17 |
| Hall | C7×C11×C17 ⋊ C9 |
| Hall | C7×C17 ⋊ C9×C11 |
| Hall | C7×C11 ⋊ C9×C17 |
24 conjugacy classes of subgroups.
2805 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C17×C7⋊C9, C11×D17×C7⋊C9, C17×D11×C7⋊C9, … |
| maximal normal subgroup of | C2×C11×C17×C7⋊C9, C11×D17×C7⋊C9, C17×D11×C7⋊C9, … |
| maximal quotient of | C2×C11×C17×C7⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11781, 2);