Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C59 ⋊ #1742 |
388 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 189 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=f,c^2=g,e^2=g,b^a=bd,d^a=dg,h^a=h^58,e^b=eg1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28475817, #28475819, #28493900, … |
| maximal normal subgroup of | #28475817, #28475819, #28493900, … |
| maximal quotient of | #28478280, #28478283, #28478292, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4249);