Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#16838203 |
| Fitting | C22×D8×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#576 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C4×C59 | C25 |
| Frattini | C4 | C24×D59 |
| Fitting | C22×D8×C59 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | C22×D8 | D59 |
| hypocenter | C59 | C2×#576 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C22×D8 | |
1512 conjugacy classes of subgroups.
856 conjugacy classes — view the full character table.
| maximal subgroup of | #28504373, #28504385, #28504412, … |
| maximal normal subgroup of | #28504373, #28504385, #28504412, … |
| maximal quotient of | C2×#21432617, C2×#21432692, C2×#21432921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19259);