Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×#14273725 |
| Sylow | C59 ⋊ C22×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C23×Q8×C59 | C2 |
| socle | C24×C59 | C23 |
| hypercenter | C23×Q8 | D59 |
| hypocenter | C59 | C22×C4⋊Q8 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C24 ◁ C23×Q8 | |
1624 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 1624 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28481321, #28495239, #28495240, … |
| maximal normal subgroup of | #28481321, #28495239, #28495240, … |
| maximal quotient of | C22×#16837271, C22×#16837297, C22×#16837307, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17784);