Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3080 |
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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=eg,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,h^a=h^58,f^c=fg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28485778, #28485780, #28485785, … |
| maximal normal subgroup of | #28485778, #28485780, #28485785, … |
| maximal quotient of | #28588191, #28589666, #28590874, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14332);