Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #106×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1922 |
186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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=f,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^11,h^b=h^11,e^c=eg,h^c=h^60,h^f=h^60248 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21461885, D61⋊#1922, #30615859, … |
| maximal normal subgroup of | C2×#21461885, D61⋊#1922, #30615859, … |
| maximal quotient of | #30601326, #30601329, #30601336, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20576);