Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C59×#346 ⋊ C2 |
| Sylow | C59 ⋊ #2244 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|b^2=eg,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^58,c^b=cg1186 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28502339, #28502340, #28502346, … |
| maximal normal subgroup of | #28502339, #28502340, #28502346, … |
| maximal quotient of | #28505075, #28506619, #28506921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6752);