Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#16838008 |
| Fitting | C2×#125×C59 ⋊ C2 |
| Sylow | C59 ⋊ C2×#540 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C2×#125×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#125 | D59 |
| hypocenter | C59 | C2×#540 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
856 conjugacy classes — view the full character table.
| maximal subgroup of | #28481224, #28593855, #28593983, … |
| maximal normal subgroup of | #28481224, #28593855, #28593983, … |
| maximal quotient of | C2×#21426706, C2×#21426735, C2×#21426787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 17871);