Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C61 ⋊ C4 |
| Sylow | C61 ⋊ C2×#347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×C4×#6923 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C8 | C22×#6923 |
| Fitting | M32×C61 | C4 |
| socle | C2×C61 | C2×#97 |
| hypercenter | M32 | #6923 |
| hypocenter | C61 | C2×#347 |
| LCS | G ▷ C4×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ M32 | |
168 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 80 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=d,b^2=e,d^2=f,f^2=g,b^a=bf,e^a=eg,d^b=dg,h^b=h^11,h^c=h^60,h^e=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #347×#6923, #30606122, #30606428, … |
| maximal normal subgroup of | #347×#6923, #30606122, #30606428, … |
| maximal quotient of | #30603700, #30603704, #30603705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20725);