Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ AΣL(1,𝔽16) |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^a=bc,c^a=ce,e^a=ef,g^a=g^112,d^b=de,d^c=df797 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽16)×D113, C2×#20298385, #28392212, … |
| maximal normal subgroup of | AΣL(1,𝔽16)×D113, C2×#20298385, #28392212, … |
| maximal quotient of | #28388502, #28388522, #28388571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 336);