Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | #538×D59 |
| Fitting | C59×#538 ⋊ C2 |
| Sylow | C59 ⋊ C2×#538 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×#538 | C2 |
| hypercenter | #538 | D59 |
| hypocenter | C59 | C2×#538 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #538 | |
1336 conjugacy classes of subgroups.
682 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1600, D59×#1606, D59×#1612, … |
| maximal normal subgroup of | D59×#1600, D59×#1606, D59×#1612, … |
| maximal quotient of | D59×#2312, D59×#2318, D59×#2321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17844);