Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | #419×D59 |
| Fitting | C59×#419 ⋊ C2 |
| Sylow | C59 ⋊ C2×#419 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C4×C59 | C23×C4 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#419 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #419 | D59 |
| hypocenter | C59 | C2×#419 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #419 | |
752 conjugacy classes of subgroups.
682 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1796, D59×#1882, #28590209, … |
| maximal normal subgroup of | D59×#1796, D59×#1882, #28590209, … |
| maximal quotient of | D59×#1479, D59×#1491, #28555133, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13013);