Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×Dic59 |
| unambiguous semidirect product | (C2×C59)⋊C43 |
| derived, Sylow | C59 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | D59 |
| commutator, hypocenter | C59 | C2×C43 |
| Frattini | C23 | C23×D59 |
| Fitting | C22×C42×C59 | C2 |
| socle | C24×C59 | C23 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C22×C42 | |
1272 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#21421928, #28478130, #336×Dic59, … |
| maximal normal subgroup of | C2×#21421928, #28478130, #336×Dic59, … |
| maximal quotient of | C43×Dic59, C2×#95×Dic59, C2×C4×C59⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6832);