Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11745689 |
| Fitting | Q82×C59 ⋊ C2 |
| Sylow | C59 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | Q82×C59 | C2 |
| hypercenter | Q82 | D59 |
| hypocenter | C59 | Q8×#41 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
775 conjugacy classes — view the full character table.
| maximal subgroup of | #28564664, #28564672, #28564679, … |
| maximal normal subgroup of | #28564664, #28564672, #28564679, … |
| maximal quotient of | C4⋊C4×#11745689, Q8×#14273685, #28748345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18093);