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×C4⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1899 |
378 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 70 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=df,c^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^50,d^b=dg,f^b=fg,h^b=h^11,h^f=h^60332 conjugacy classes — view the full character table.
| maximal subgroup of | #30598622, #30598624, #30598626, … |
| maximal normal subgroup of | #30598622, #30598624, #30598626, … |
| maximal quotient of | #30600187, #30600188, #30600193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20534);