Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C59×D4⋊C8 ⋊ C2 |
| Sylow | C59 ⋊ #1594 |
176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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=ef,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,c^b=cg,d^b=df,h^c=h^58844 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1594, C2×#21423007, #28558461, … |
| maximal normal subgroup of | D59×#1594, C2×#21423007, #28558461, … |
| maximal quotient of | #28479522, #28479526, #28479947, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3421);