Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1512 |
222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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,c^2=f,d^2=g,b^a=bd,c^a=cg,d^a=df,d^b=dg,e^b=efg,h^c=h^60596 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1512, C2×#21444354, #29647257, … |
| maximal normal subgroup of | D61×#1512, C2×#21444354, #29647257, … |
| maximal quotient of | #29568095, #29568105, #29568125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3045);