Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#324 ⋊ C2 |
| Sylow | C59 ⋊ #1468 |
280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 280 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,e^2=g,b^a=bd,d^a=df,c^b=cg,e^b=ef,h^b=h^58,h^c=h^58670 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1468, C2×#21422443, #28554646, … |
| maximal normal subgroup of | D59×#1468, C2×#21422443, #28554646, … |
| maximal quotient of | #28477020, #28477023, #28477040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2857);