Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16837425 |
| Sylow | C59 ⋊ C2×#423 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C22×M16×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| hypercenter | C22×M16 | D59 |
| hypocenter | C59 | C2×#423 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
576 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28494488, Dic59⋊#338, #28494498, … |
| maximal normal subgroup of | #28494488, Dic59⋊#338, #28494498, … |
| maximal quotient of | C2×#21422851, C2×#21422854, C2×#21422857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13064);