Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16837655 |
| Fitting | C22×M16×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#469 |
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#21422080, C2×#21422082, C2×#21422086, … |
| maximal normal subgroup of | C2×#21422080, C2×#21422082, C2×#21422086, … |
| maximal quotient of | C2×#21423575, C2×#21423609, C2×#21423657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14106);