Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C59 ⋊ #2230 |
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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=df,b^2=d,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=ef,f^a=fg,h^b=h^58,e^c=efg,f^c=fg487 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2230, C2×#21426265, #28743429, … |
| maximal normal subgroup of | D59×#2230, C2×#21426265, #28743429, … |
| maximal quotient of | #28504788, #28505384, #28505388, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6679);