Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#552 ⋊ C2 |
| Sylow | C59 ⋊ #3327 |
380 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=eg,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^58754 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3327, C2×#21436358, #29465641, … |
| maximal normal subgroup of | D59×#3327, C2×#21436358, #29465641, … |
| maximal quotient of | #28604309, #28605097, #28605994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16772);