Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C179 ⋊ #492 |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^b=g^1781268 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37507164, #37508070, #37508071, … |
| maximal normal subgroup of | #37507164, #37508070, #37508071, … |
| maximal quotient of | #37508586, #37508589, #37508594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 921);