Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16838216 |
| Fitting | C2×#135×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#578 |
1408 conjugacy classes of subgroups.
856 conjugacy classes — view the full character table.
| maximal subgroup of | #28504380, #28504388, #28504417, … |
| maximal normal subgroup of | #28504380, #28504388, #28504417, … |
| maximal quotient of | C2×#21432625, C2×#21432693, C2×#21432932, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19274);