Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | C2×#16836604 |
| Sylow | C233 ⋊ C2×M16 |
68 conjugacy classes of subgroups.
484 conjugacy classes — view the full character table.
| maximal subgroup of | #28417305, #28417311, #28417318, … |
| maximal normal subgroup of | #28417305, #28417311, #28417318, … |
| maximal quotient of | C2×#21418590, C4×#16836604, C2×#21418592, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 232);