Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #123×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1913 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16840710 |
| commutator | C23×C61 | C22×C4 |
| Frattini | C23 | C22×#6923 |
| Fitting | #123×C61 | C4 |
| socle | C2×C61 | #386 |
| hypercenter | #123 | #6923 |
| hypocenter | C61 | #1913 |
| LCS | G ▷ C23×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #123 | |
380 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 66 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=df,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^50,d^b=dg,e^b=eg,f^b=fg,h^b=h^11,d^c=dg,f^c=fg,h^f=h^60239 conjugacy classes — view the full character table.
| maximal subgroup of | #30606985, #30606986, #30606989, … |
| maximal normal subgroup of | #30606985, #30606986, #30606989, … |
| maximal quotient of | #30600295, #30600296, #30600297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20560);