Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#537 ⋊ C2 |
| Sylow | C59 ⋊ #3204 |
402 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=g,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#3204, C2×#21435002, #29459412, … |
| maximal normal subgroup of | D59×#3204, C2×#21435002, #29459412, … |
| maximal quotient of | #28597800, #28597806, #28598994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15416);