Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C59×#532 ⋊ C2 |
| Sylow | C59 ⋊ #3529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D59 |
| commutator, socle | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C59×#532 | C2 |
| hypercenter | #532 | D59 |
| hypocenter | C59 | #3529 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1058 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|e^2=f,b^a=bf,c^a=cg,d^a=dfg,c^b=cfg,d^b=df,h^d=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | #28481121, #28481124, #28504526, … |
| maximal normal subgroup of | #28481121, #28481124, #28504526, … |
| maximal quotient of | #28751300, #28751302, #28751328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18646);