Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | #126×Dic59 |
| Sylow | C59 ⋊ C4×#126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C2×#126×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#126 | D59 |
| hypocenter | C59 | C4×#126 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#126 | |
516 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
868 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#126×D59, C2×#126×Dic59, C4×#16837935, … |
| maximal normal subgroup of | C4×#126×D59, C2×#126×Dic59, C4×#16837935, … |
| maximal quotient of | #388×Dic59, #387×Dic59, #383×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7062);