Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16837831 |
| Fitting | C2×D16×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
682 conjugacy classes — view the full character table.
| maximal subgroup of | #28509120, #28509125, #28509162, … |
| maximal normal subgroup of | #28509120, #28509125, #28509162, … |
| maximal quotient of | C2×#21425800, C2×#21425877, C2×D16×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17625);