Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q16×Dic113 |
| Sylow | C113 ⋊ C4×Q16 |
110 conjugacy classes of subgroups.
812 conjugacy classes — view the full character table.
| maximal subgroup of | #28392423, SD32×Dic113, #28392430, … |
| maximal normal subgroup of | #28392423, SD32×Dic113, #28392430, … |
| maximal quotient of | Q16×#11744751, #28389425, #28389471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 644);