Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C179 ⋊ #384 |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=f,b^2=d,c^2=e,b^a=bd,c^a=ce,g^c=g^1781808 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37506945, #37508998, #37508999, … |
| maximal normal subgroup of | #37506945, #37508998, #37508999, … |
| maximal quotient of | #37507228, #37507229, #37507263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 418);