Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#16838138 |
| Sylow | C59 ⋊ C2×#559 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C2×#127×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#127 | D59 |
| hypocenter | C59 | C2×#559 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
1240 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1240 conjugacy classes of subgroups — too many to draw. Only its 501 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
862 conjugacy classes — view the full character table.
| maximal subgroup of | #28480404, #28480765, #28480769, … |
| maximal normal subgroup of | #28480404, #28480765, #28480769, … |
| maximal quotient of | C2×#21427055, C2×#21427068, C2×#21427161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18099);