Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C59 ⋊ #2241 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,b^2=e,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,h^a=h^581894 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28502311, #28502312, #28502318, … |
| maximal normal subgroup of | #28502311, #28502312, #28502318, … |
| maximal quotient of | #28505069, #28506612, #28506907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6738);