Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C59⋊C16 |
| derived, Sylow | C59 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | D59 |
| commutator, hypocenter | C59 | C2×C4×C16 |
| Frattini | C2×C8 | C22×D59 |
| Fitting | C2×C4×C8×C59 | C2 |
| socle | C23×C59 | C2×C8 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C4×C8 | |
216 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475516, #28475517, #28475528, … |
| maximal normal subgroup of | #28475516, #28475517, #28475528, … |
| maximal quotient of | C2×C8×C59⋊C16, C2×#21422014, M16×C59⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6097);