Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | #343×D59 |
| Fitting | C59×#343 ⋊ C2 |
| Sylow | C59 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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 | D59×#1345, D59×#1346, #28498893, … |
| maximal normal subgroup of | D59×#1345, D59×#1346, #28498893, … |
| maximal quotient of | D59×#1280, #28478284, #28478287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4244);