Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#448 ⋊ C2 |
| Sylow | C59 ⋊ #3320 |
388 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=eg,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,c^b=cg,d^b=de,h^b=h^58,f^c=fg580 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3320, C2×#21436271, #29465451, … |
| maximal normal subgroup of | D59×#3320, C2×#21436271, #29465451, … |
| maximal quotient of | #28604263, #28605005, #28605799, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16685);