Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C179 ⋊ #407 |
190 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^1782876 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37506852, #37506853, #37506876, … |
| maximal normal subgroup of | #37506852, #37506853, #37506876, … |
| maximal quotient of | #37507327, #37507330, #37507334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 513);