Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#332 ⋊ C2 |
| Sylow | C59 ⋊ #1540 |
256 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=e,c^2=f,d^2=g,e^2=fg,b^a=bd,d^a=df,d^b=dg,e^b=efg,h^b=h^58,h^c=h^58589 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1540, C2×#21422744, #28557001, … |
| maximal normal subgroup of | D59×#1540, C2×#21422744, #28557001, … |
| maximal quotient of | #28476627, #28476647, #28476973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3158);