Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×#328 ⋊ C2 |
| Sylow | C61 ⋊ #1618 |
240 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 49 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=fg,c^2=fg,d^2=f,b^a=bd,c^a=ce,d^a=df,h^a=h^60,d^b=df,e^b=eg,h^b=h^60,d^c=dg,h^c=h^60593 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1618, C2×#21444870, #29652271, … |
| maximal normal subgroup of | D61×#1618, C2×#21444870, #29652271, … |
| maximal quotient of | #29569064, #29569086, #29569106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3561);