Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ D4⋊C8 |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^98,c^b=ce,g^b=g^112,g^d=g^112308 conjugacy classes — view the full character table.
| maximal subgroup of | #28405860, C2×#20299446, #28405867, … |
| maximal normal subgroup of | #28405860, C2×#20299446, #28405867, … |
| maximal quotient of | #28405391, #28405393, #28405410, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1397);