Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C4×(C22⋊D59)⋊C4 |
| Fitting | C4×C22⋊C4×C59 ⋊ C2 |
| Sylow | C59 ⋊ C42×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D59 |
| commutator | C2×C59 | C22×C42 |
| Frattini | C23 | C23×D59 |
| Fitting | C4×C22⋊C4×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C4×C22⋊C4 | D59 |
| hypocenter | C59 | C42×D4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
924 conjugacy classes of subgroups.
1240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×(C22⋊D59)⋊C4, #28587032, #28587037, … |
| maximal normal subgroup of | C8×(C22⋊D59)⋊C4, #28587032, #28587037, … |
| maximal quotient of | C4×#16837249, C4×C22⋊C4×Dic59, C4×#16837253, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6854);