Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1481 |
216 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 216 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=e,b^2=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^11,c^b=cg,d^b=df,h^c=h^60,h^e=h^60248 conjugacy classes — view the full character table.
| maximal subgroup of | #30598488, #30598489, #30598492, … |
| maximal normal subgroup of | #30598488, #30598489, #30598492, … |
| maximal quotient of | #30595666, #30595685, #30595692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19819);