Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C179 ⋊ C2 |
| Sylow | C179 ⋊ #508 |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|c^2=f,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^178,d^b=de,e^b=ef,g^b=g^178,g^c=g^1781001 conjugacy classes — view the full character table.
| maximal subgroup of | #37511308, #37511310, #37511314, … |
| maximal normal subgroup of | #37511308, #37511310, #37511314, … |
| maximal quotient of | #37510706, #37510781, #37510846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 982);