Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1762 |
388 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 100 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=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^b=h^11,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #30598451, #30598452, #30598453, … |
| maximal normal subgroup of | #30598451, #30598452, #30598453, … |
| maximal quotient of | #30597549, #30597550, #30597555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20280);