Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#343 ⋊ C2 |
| Sylow | C59 ⋊ #2027 |
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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=d,b^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^58,c^b=cf,e^b=eg,e^c=eg,h^c=h^58664 conjugacy classes — view the full character table.
| maximal subgroup of | #28501441, #28501446, #28501459, … |
| maximal normal subgroup of | #28501441, #28501446, #28501459, … |
| maximal quotient of | #28491660, #28491675, #28491680, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 5667);