Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C179 ⋊ #383 |
138 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=f,b^2=de,c^2=d,b^a=bd,c^a=ce,g^a=g^1782876 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37506865, #37506866, #37507547, … |
| maximal normal subgroup of | #37506865, #37506866, #37507547, … |
| maximal quotient of | #37507227, #37507262, #37509143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 417);