Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#16838148 |
| Fitting | C2×C22⋊Q8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#562 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C2×C22⋊Q8×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×C22⋊Q8 | D59 |
| hypocenter | C59 | C2×#562 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊Q8 | |
1152 conjugacy classes of subgroups.
850 conjugacy classes — view the full character table.
| maximal subgroup of | #28751384, C4×#16838148, #28754519, … |
| maximal normal subgroup of | #28751384, C4×#16838148, #28754519, … |
| maximal quotient of | C2×#21427240, C2×#21427241, C2×#21427243, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18635);