Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C4⋊C8×C59 ⋊ C2 |
| Sylow | C59 ⋊ #1540 |
256 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 89 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,h^a=h^58,d^b=dg,e^b=efg,h^b=h^581198 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28479753, #28479758, #28479767, … |
| maximal normal subgroup of | #28479753, #28479758, #28479767, … |
| maximal quotient of | #28476629, #28476646, #28476975, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3160);