Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11744762 |
| Fitting | C2×C4×C113 ⋊ C8 |
| Sylow | C113 ⋊ C2×C4⋊C8 |
138 conjugacy classes of subgroups.
152 conjugacy classes — view the full character table.
| maximal subgroup of | #28407580, #28407582, #28407586, … |
| maximal normal subgroup of | #28407580, #28407582, #28407586, … |
| maximal quotient of | C2×#20299687, C2×#20299688, #28407698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1661);