Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C4⋊C8×D179 |
| Fitting | C4⋊C8×C179 ⋊ C2 |
| Sylow | C179 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊C8×D179, Q8⋊C8×D179, #37507384, … |
| maximal normal subgroup of | D4⋊C8×D179, Q8⋊C8×D179, #37507384, … |
| maximal quotient of | #334×D179, #335×D179, #37507745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 568);