Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×SD16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3301 |
398 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,d^b=de,h^b=h^58,f^c=fg,h^d=h^58847 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3301, C2×#21436003, #29465174, … |
| maximal normal subgroup of | D59×#3301, C2×#21436003, #29465174, … |
| maximal quotient of | #28604137, #28604945, #28605879, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16417);