Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×D8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1970 |
384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,b^2=dfg,c^2=eg,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^50,h^b=h^11,h^f=h^60254 conjugacy classes — view the full character table.
| maximal subgroup of | #30607569, #30607570, #30607592, … |
| maximal normal subgroup of | #30607569, #30607570, #30607592, … |
| maximal quotient of | #30601672, #30601673, #30601674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20657);