Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1757 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊C4×#6923 |
| commutator | C22×C61 | C2×C42 |
| Frattini | C23 | C22×#6923 |
| Fitting | #99×C61 | C4 |
| socle | C2×C61 | C4×C22⋊C4 |
| hypercenter | #99 | #6923 |
| hypocenter | C61 | #1757 |
| LCS | G ▷ C22×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
284 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 86 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,b^2=f,c^2=e,e^2=g,b^a=bd,f^a=fg,h^a=h^50,d^b=dg,h^c=h^11,h^e=h^60209 conjugacy classes — view the full character table.
| maximal subgroup of | #30606519, #30606522, #30606525, … |
| maximal normal subgroup of | #30606519, #30606522, #30606525, … |
| maximal quotient of | #30597475, #30597478, #30597481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20268);