Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C42×C59⋊C8 |
| derived, Sylow | C59 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D59 |
| commutator, hypocenter | C59 | C42×C8 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C43×C59 | C2 |
| socle | C23×C59 | C22×C4 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C43 | |
408 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475216, C4×C8×C59⋊C8, C4×#16837123, … |
| maximal normal subgroup of | #28475216, C4×C8×C59⋊C8, C4×#16837123, … |
| maximal quotient of | C4×C8×C59⋊C8, C4×#16837123, #97×C59⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4192);