Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1515 |
208 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 69 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,b^2=f,c^2=fg,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^58,d^b=dg,e^b=efg,h^b=h^58838 conjugacy classes — view the full character table.
| maximal subgroup of | #28481100, #28481101, #28481103, … |
| maximal normal subgroup of | #28481100, #28481101, #28481103, … |
| maximal quotient of | #28476780, #28476814, #28476816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3062);