Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C179 ⋊ #423 |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=e,b^2=d,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 | #37506858, #37506859, #37506874, … |
| maximal normal subgroup of | #37506858, #37506859, #37506874, … |
| maximal quotient of | #37507756, #37507759, #37507763, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 573);