Finite Group DatabasebetaFinite Group Databasebeta| order | 11456 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #99×C179 ⋊ C2 |
| Sylow | C179 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,179|a^2=d,b^a=bc,c^a=ce,e^a=ef,d^b=de,g^b=g^178,d^c=df992 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D179, C2×#26038225, #37510639, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D179, C2×#26038225, #37510639, … |
| maximal quotient of | #37506927, #37506947, #37506996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11456, 335);