Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C61 ⋊ #1720 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14519773 |
| commutator | C42×C61 | C23 |
| Frattini | C42 | C22×D61 |
| Fitting | C61×#486 | C2 |
| socle | C22×C61 | #127 |
| hypercenter | #486 | D61 |
| hypocenter | C61 | #1720 |
| LCS | G ▷ C42×C61 ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #486 | |
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 57 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=dfg,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,c^b=cf,h^b=h^60,h^c=h^60686 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1720, C2×#21445478, #29667785, … |
| maximal normal subgroup of | D61×#1720, C2×#21445478, #29667785, … |
| maximal quotient of | #29573811, #29579795, #29579802, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 4169);