Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
| direct product | C2×C59⋊#338 |
| unambiguous semidirect product | (C2×C59)⋊#338 |
| Sylow | C59 ⋊ C2×#338 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic59 |
| commutator | C4×C59 | C2×C42 |
| Frattini | C22×C4 | C22×D59 |
| Fitting | C22×M16×C59 | C2 |
| socle | C22×C59 | #95 |
| hypercenter | C22×M16 | D59 |
| hypocenter | C59 | C2×#338 |
| LCS | G ▷ C4×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C22×M16 | |
372 conjugacy classes of subgroups.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475823, #28475825, #28475829, … |
| maximal normal subgroup of | #28475823, #28475825, #28475829, … |
| maximal quotient of | C2×#21421926, C2×#21421927, #28478107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4213);