Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3166 |
348 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 165 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,c^2=f,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^c=dg1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28486312, #28489601, #28489603, … |
| maximal normal subgroup of | #28486312, #28489601, #28489603, … |
| maximal quotient of | #28589124, #28592079, #28593278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15062);