Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #3095 |
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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=g,c^2=e,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 | #28485743, #28485745, #28485855, … |
| maximal normal subgroup of | #28485743, #28485745, #28485855, … |
| maximal quotient of | #28588500, #28589437, #28589931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14458);