Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×D179 |
| Fitting | C4×Q8×C179 ⋊ C2 |
| Sylow | C179 ⋊ C2×C4×Q8 |
298 conjugacy classes of subgroups.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q8⋊C8×D179, #37507393, #37507427, … |
| maximal normal subgroup of | Q8⋊C8×D179, #37507393, #37507427, … |
| maximal quotient of | C4×C4⋊C4×D179 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 1012);