Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C61×#328 ⋊ C2 |
| Sylow | C61 ⋊ #1520 |
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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=g,d^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cf,d^b=dg,e^b=efg,h^c=h^60602 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1520, C2×#21444389, #29647337, … |
| maximal normal subgroup of | D61×#1520, C2×#21444389, #29647337, … |
| maximal quotient of | #29568009, #29568013, #29568075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3080);