Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C59 ⋊ C2 |
| Sylow | C59 ⋊ #3021 |
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,e^b=eg,f^b=fg,e^c=eg,h^c=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | #28620094, #28620097, #28620116, … |
| maximal normal subgroup of | #28620094, #28620097, #28620116, … |
| maximal quotient of | #28561080, #28561127, #28561158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 13879);