Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| isoclinism | isoclinic class of D59 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C64×D59 |
| Fitting | C59×C64 ⋊ C2 |
| derived, Sylow | C59 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D59 |
| commutator, hypocenter | C59 | C2×C64 |
| Frattini | C32 | C2×D59 |
| Fitting | C59×C64 | C2 |
| socle | C2×C59 | C2×C32 |
| LCS | G ▷ C59 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
1984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×C128, #28476599, C2×C64×D59, … |
| maximal normal subgroup of | D59×C128, #28476599, C2×C64×D59, … |
| maximal quotient of | C64×Dic59, (C2×D59)⋊C64, Dic59⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2718);