Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D8×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2011 |
510 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,c^b=cf,d^b=dg,e^b=eg,d^c=dg,e^c=eg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2011, C2×#21446888, #29707080, … |
| maximal normal subgroup of | D61×#2011, C2×#21446888, #29707080, … |
| maximal quotient of | #29580430, #29580431, #29580472, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5579);