Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C61×C22⋊C16 ⋊ C2 |
| Sylow | C61 ⋊ #1315 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^601238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#1315, C2×#21443744, #29589083, … |
| maximal normal subgroup of | D61×#1315, C2×#21443744, #29589083, … |
| maximal quotient of | #29566639, #29566641, #29566643, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2435);