Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #533×D59 |
| Fitting | C59×#533 ⋊ C2 |
| Sylow | C59 ⋊ C2×#533 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C59×#533 | C2 |
| hypercenter | #533 | D59 |
| hypocenter | C59 | C2×#533 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #533 | |
1168 conjugacy classes of subgroups.
868 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1481, D59×#1485, #28555233, … |
| maximal normal subgroup of | D59×#1481, D59×#1485, #28555233, … |
| maximal quotient of | D59×#2285, D59×#2295, D59×#2296, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17795);