Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C59 ⋊ C4×C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D59 |
| commutator | C22×C59 | C23×C4 |
| Fitting | C59×#389 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | #389 | D59 |
| hypocenter | C59 | C4×C4⋊Q8 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ #389 | |
588 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=e,c^2=f,d^2=eg,b^a=be,c^a=cf,h^b=h^58,h^d=h^58868 conjugacy classes — view the full character table.
| maximal subgroup of | #28476665, #28476747, #28476760, … |
| maximal normal subgroup of | #28476665, #28476747, #28476760, … |
| maximal quotient of | #28509879, #28509881, #389×Dic59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 7081);