Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | Q82×C59 ⋊ C2 |
| Sylow | C59 ⋊ #2205 |
224 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=g,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^58,c^b=cg,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg745 conjugacy classes — view the full character table.
| maximal subgroup of | #28509456, #28509457, #28509461, … |
| maximal normal subgroup of | #28509456, #28509457, #28509461, … |
| maximal quotient of | #28500781, #28500946, #28501055, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6540);