Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C59×#346 ⋊ C2 |
| Sylow | C59 ⋊ #1330 |
100 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,c^2=eg,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^58,c^b=ceg,d^b=dg,h^b=h^581198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1330, C2×#21422055, #28498406, … |
| maximal normal subgroup of | D59×#1330, C2×#21422055, #28498406, … |
| maximal quotient of | #28475351, #28475354, #28475357, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2469);