Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C8×C22⋊D179 |
| Fitting | C22×C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ C8×D4 |
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37510817, C16×C22⋊D179, #37510822, … |
| maximal normal subgroup of | #37510817, C16×C22⋊D179, #37510822, … |
| maximal quotient of | C8×#15668244, C8×#15668247, C8×#15668246, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 613);