Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C179 ⋊ #328 |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^2=e,c^2=f,b^a=bc,c^a=ce,g^a=g^178,c^b=cf,d^b=def1265 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #328×D179, C2×#26038176, #37507485, … |
| maximal normal subgroup of | #328×D179, C2×#26038176, #37507485, … |
| maximal quotient of | #37506823, #37506826, #37506878, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 286);