Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C59 ⋊ #2151 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D59 |
| commutator, socle | C22×C59 | C22×C8 |
| Fitting | C2×M32×C59 | C2 |
| hypercenter | C2×M32 | D59 |
| hypocenter | C59 | #2151 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C2×C8 ◁ C2×M32 | |
160 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^58,c^b=cg,h^b=h^581216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28476093, #28504825, #28504828, … |
| maximal normal subgroup of | #28476093, #28504825, #28504828, … |
| maximal quotient of | #28500238, #28500264, #28500298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6270);