Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×Dic59⋊C4 |
| Sylow | C59 ⋊ C23×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D59 |
| commutator | C2×C59 | C24×C4 |
| Frattini | C22 | C24×D59 |
| Fitting | C24×C4×C59 | C2 |
| socle | C25×C59 | C22 |
| hypercenter | C24×C4 | D59 |
| hypocenter | C59 | C23×C4⋊C4 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
2488 conjugacy classes of subgroups.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476615, #28480018, C2×Dic59⋊#95, … |
| maximal normal subgroup of | #28476615, #28480018, C2×Dic59⋊#95, … |
| maximal quotient of | C23×C59⋊#95, C22×C4×Dic59⋊C4, C22×#16837260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17670);