Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C24×C59⋊C8 |
| derived, Sylow | C59 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D59 |
| commutator, hypocenter | C59 | C24×C8 |
| Frattini | C4 | C24×D59 |
| Fitting | C24×C4×C59 | C2 |
| socle | C25×C59 | C4 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C24×C4 | |
1976 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28493912, #28493914, #28493938, … |
| maximal normal subgroup of | #28493912, #28493914, #28493938, … |
| maximal quotient of | C23×C4×C59⋊C8, C23×C22⋊(C59⋊C8), C23×C4⋊(C59⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19209);