Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C59⋊C32 |
| derived, Sylow | C59 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D59 |
| commutator, hypocenter | C59 | C22×C32 |
| Frattini | C16 | C22×D59 |
| Fitting | C22×C16×C59 | C2 |
| socle | C23×C59 | C16 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476375, #28476376, #28476387, … |
| maximal normal subgroup of | #28476375, #28476376, #28476387, … |
| maximal quotient of | C2×C4×C59⋊C32, C2×C22⋊(C59⋊C32), C2×C4⋊(C59⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6799);