Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1736 |
448 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=e,b^2=f,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28494015, #28494016, #28494050, … |
| maximal normal subgroup of | #28494015, #28494016, #28494050, … |
| maximal quotient of | #28478150, #28478160, #28478172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 4229);