Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #2162 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×#6923 |
| commutator | C2×C61 | C22×C16 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | C4×C8×C61 | C4 |
| socle | C22×C61 | C22×C8 |
| hypercenter | C4×C8 | #6923 |
| hypocenter | C61 | #2162 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
160 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 78 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=e,c^2=d,e^2=f,f^2=g,b^a=bd,h^a=h^11,h^b=h^60,h^e=h^60560 conjugacy classes — view the full character table.
| maximal subgroup of | #30594190, #30594199, #30594200, … |
| maximal normal subgroup of | #30594190, #30594199, #30594200, … |
| maximal quotient of | #30606342, C4×#16840657, C4×#16840683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20869);