Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q16×C59⋊C8 |
| Sylow | C59 ⋊ C8×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D59 |
| commutator | C4×C59 | C22×C8 |
| Frattini | C42 | C22×D59 |
| Fitting | C4×Q16×C59 | C2 |
| socle | C22×C59 | C4×D4 |
| hypercenter | C4×Q16 | D59 |
| hypocenter | C59 | C8×Q16 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ C4×Q16 | |
164 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
868 conjugacy classes — view the full character table.
| maximal subgroup of | #28500413, SD32×C59⋊C8, #28500420, … |
| maximal normal subgroup of | #28500413, SD32×C59⋊C8, #28500420, … |
| maximal quotient of | #103×C59⋊C8, #107×C59⋊C8, #28482609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3317);