Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C16×C59⋊C8 |
| derived, Sylow | C59 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | D59 |
| commutator, hypocenter | C59 | C8×C16 |
| Frattini | C4×C8 | C2×D59 |
| Fitting | C4×C16×C59 | C2 |
| socle | C22×C59 | C4×C8 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C4×C16 | |
104 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C59⋊C8, #28476016, #28476021, … |
| maximal normal subgroup of | C32×C59⋊C8, #28476016, #28476021, … |
| maximal quotient of | C16×C59⋊C16, #28475304, #28475516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2424);