Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C179⋊#338 |
| Sylow | C179 ⋊ #338 |
86 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^1781802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37506991, #37506992, #37506994, … |
| maximal normal subgroup of | #37506991, #37506992, #37506994, … |
| maximal quotient of | #37506830, #37506831, #37506871, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 307);