Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1772 |
232 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 90 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,c^2=de,d^2=g,b^a=bd,d^b=dg,e^b=eg,h^b=h^11,h^f=h^60536 conjugacy classes — view the full character table.
| maximal subgroup of | #30594310, #30594311, #30594314, … |
| maximal normal subgroup of | #30594310, #30594311, #30594314, … |
| maximal quotient of | #30597981, #30597983, #30597985, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20312);