Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×Q16×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3172 |
364 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,h^b=h^58,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | #28559281, #28559285, #28559301, … |
| maximal normal subgroup of | #28559281, #28559285, #28559301, … |
| maximal quotient of | #28589241, #28592931, #28592933, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 15114);