Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D61⋊#328 |
| Fitting | C22⋊Q8×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#328 |
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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=e,b^2=f,d^2=g,b^a=bd,d^a=df,h^a=h^11,d^b=dg,e^b=efg,h^c=h^60,h^e=h^60248 conjugacy classes — view the full character table.
| maximal subgroup of | #328×#6923, #30597750, #30597760, … |
| maximal normal subgroup of | #328×#6923, #30597750, #30597760, … |
| maximal quotient of | D61⋊#1271, D61⋊#1272, #30595354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19879);