Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C59×#364 ⋊ C2 |
| Sylow | C59 ⋊ #1336 |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,c^b=ceg,d^b=dg,e^b=eg,h^b=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1336, C2×#21422071, #28498482, … |
| maximal normal subgroup of | D59×#1336, C2×#21422071, #28498482, … |
| maximal quotient of | #28475343, #28475346, #28475349, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2485);