Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#16837304 |
| Fitting | C22×C42×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#390 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C22×C59 | C23×C4 |
| Frattini | C23 | C23×D59 |
| Fitting | C22×C42×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C22×C42 | D59 |
| hypocenter | C59 | C2×#390 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C22×C42 | |
1360 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#21421916, #28476673, #28476675, … |
| maximal normal subgroup of | C2×#21421916, #28476673, #28476675, … |
| maximal quotient of | C2×#21422326, C2×#21422334, C4×#16837304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6966);