Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C2×C32×D59 |
| Fitting | C2×C32×C59 ⋊ C2 |
| derived, Sylow | C59 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D59 |
| commutator, hypocenter | C59 | C22×C32 |
| Frattini | C16 | C22×D59 |
| Fitting | C2×C32×C59 | C2 |
| socle | C22×C59 | C2×C16 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C2×C32 | |
120 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D59)⋊C64, C4×C32×D59, D59×#1397, … |
| maximal normal subgroup of | (C2×D59)⋊C64, C4×C32×D59, D59×#1397, … |
| maximal quotient of | C4×C32×D59, C2×C32×Dic59, D59×C22⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6798);