Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #1593 |
148 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^58,c^b=cg,d^b=df,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28500641, #28500643, #28500655, … |
| maximal normal subgroup of | #28500641, #28500643, #28500655, … |
| maximal quotient of | #28479531, #28479950, #28482651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3419);