Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C59×Q8⋊C8 ⋊ C2 |
| Sylow | C59 ⋊ #1582 |
168 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 63 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=e,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^58,d^b=df,h^b=h^58,h^c=h^58850 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1582, C2×#21422935, #28558219, … |
| maximal normal subgroup of | D59×#1582, C2×#21422935, #28558219, … |
| maximal quotient of | #28479480, #28479547, #28479968, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3349);