Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C59⋊C16) |
| Sylow | C59 ⋊ C2×C4⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D59 |
| commutator | C2×C59 | C22×C16 |
| Frattini | C2×C8 | C22×D59 |
| Fitting | C2×C4×C8×C59 | C2 |
| socle | C23×C59 | C2×C8 |
| hypercenter | C2×C4×C8 | D59 |
| hypocenter | C59 | C2×C4⋊C16 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22×C8 ◁ C2×C4×C8 | |
184 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475551, #28475552, #28475555, … |
| maximal normal subgroup of | #28475551, #28475552, #28475555, … |
| maximal quotient of | C2×#21422160, C2×#21422166, #28500289, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6263);