Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#449 ⋊ C2 |
| Sylow | C59 ⋊ #3319 |
414 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=eg,b^2=g,d^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×#3319, C2×#21436256, #29465449, … |
| maximal normal subgroup of | D59×#3319, C2×#21436256, #29465449, … |
| maximal quotient of | #28604248, #28604990, #28605766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16670);