Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1985 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C22×Q8×C61 | C4 |
| hypercenter | C22×Q8 | #6923 |
| hypocenter | C61 | #1985 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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=f,b^2=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^50,c^b=cg,h^b=h^11,h^c=h^60,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #30594761, #30598550, #30598552, … |
| maximal normal subgroup of | #30594761, #30598550, #30598552, … |
| maximal quotient of | #30602134, #30602137, #30602140, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20684);