Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD32×C179 ⋊ C2 |
| Sylow | C179 ⋊ #509 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,g^a=g^178,d^b=de,e^b=ef,g^c=g^178995 conjugacy classes — view the full character table.
| maximal quotient of | #37510711, #37510714, #37510787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 986);