Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#103×C61 ⋊ C2 |
| Sylow | C61 ⋊ #2035 |
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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=g,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,h^b=h^60,e^c=eg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2035, C2×#21447014, #29707493, … |
| maximal normal subgroup of | D61×#2035, C2×#21447014, #29707493, … |
| maximal quotient of | #29583308, #29583329, #29583398, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5705);