Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×#368 ⋊ C2 |
| Sylow | C59 ⋊ #2161 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,h^c=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | #28509647, #28509650, #28509652, … |
| maximal normal subgroup of | #28509647, #28509650, #28509652, … |
| maximal quotient of | #28500275, #28500277, #28500339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6303);