Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D59)⋊C32 |
| Fitting | C2×C32×C59 ⋊ C2 |
| Sylow | C59 ⋊ C22⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C2×D59 |
| commutator | C2×C59 | C2×C32 |
| Fitting | C2×C32×C59 | C2 |
| socle | C22×C59 | C2×C16 |
| hypercenter | C2×C32 | D59 |
| hypocenter | C59 | C22⋊C32 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C16 ◁ C2×C32 | |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^581936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×C22⋊C32, C2×(C2×D59)⋊C32, #28508881, … |
| maximal normal subgroup of | D59×C22⋊C32, C2×(C2×D59)⋊C32, #28508881, … |
| maximal quotient of | #28476027, #28476087, #28476126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2647);