Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#104×C59 ⋊ C2 |
| Sylow | C59 ⋊ #1896 |
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=f,b^2=df,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1896, C2×#21424536, #28590451, … |
| maximal normal subgroup of | D59×#1896, C2×#21424536, #28590451, … |
| maximal quotient of | #28484017, #28484022, #28484047, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4950);