Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #564×D59 |
| Fitting | C59×#564 ⋊ C2 |
| Sylow | C59 ⋊ C2×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×#564 | C2 |
| hypercenter | #564 | D59 |
| hypocenter | C59 | C2×#564 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #564 | |
896 conjugacy classes of subgroups.
589 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1658, D59×#1663, #28569989, … |
| maximal normal subgroup of | D59×#1658, D59×#1663, #28569989, … |
| maximal quotient of | D59×#2382, #28751409, #564×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18652);