Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1288 |
152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 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,b^2=e,c^2=fg,e^2=g,b^a=bc,c^a=cf,e^a=efg,h^a=h^11,d^b=dg,h^d=h^60512 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460679, #30596593, #30596598, … |
| maximal normal subgroup of | C2×#21460679, #30596593, #30596598, … |
| maximal quotient of | #30593929, #30593939, #30593942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19370);