Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | AGL(1,ℤ/8)×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2956 |
458 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=f,c^2=f,e^2=g,f^2=g,b^a=be,e^a=eg,h^a=h^50,e^b=eg,d^c=dg,h^c=h^11,h^f=h^60209 conjugacy classes — view the full character table.
| maximal subgroup of | #30621803, #30621804, #30621807, … |
| maximal normal subgroup of | #30621803, #30621804, #30621807, … |
| maximal quotient of | #30612315, #30612316, #30612318, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21284);