Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×(C2×D59)⋊C4 |
| Fitting | C24×C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ C23×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C24×C4×C59 | C2 |
| socle | C25×C59 | C22 |
| hypercenter | C24×C4 | D59 |
| hypocenter | C59 | C23×C22⋊C4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
4632 conjugacy classes of subgroups; only the 1413 normal subgroups are shown.
This group has 4632 conjugacy classes of subgroups — too many to draw. Only its 1413 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476610, #28480015, C2×(C2×D59)⋊#95, … |
| maximal normal subgroup of | #28476610, #28480015, C2×(C2×D59)⋊#95, … |
| maximal quotient of | C23×C59⋊#95, C22×C4×(C2×D59)⋊C4, C22×#16837257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17667);