Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×(C2×D179)⋊C4 |
| Fitting | C2×C42×C179 ⋊ C2 |
| Sylow | C179 ⋊ C4×C22⋊C4 |
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #37508770, C8×(C2×D179)⋊C4, #37508775, … |
| maximal normal subgroup of | #37508770, C8×(C2×D179)⋊C4, #37508775, … |
| maximal quotient of | C4×C179⋊#95, #37507221, #37507224, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 398);