Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | M32×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2108 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#6923 |
| commutator, socle | C2×C61 | C2×C4×C8 |
| Fitting | M32×C61 | C4 |
| hypercenter | M32 | #6923 |
| hypocenter | C61 | #2108 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ M32 | |
184 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 96 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,h^a=h^50,c^b=cg,h^b=h^11,h^d=h^60,h^e=h^60380 conjugacy classes — view the full character table.
| maximal subgroup of | #30606132, #30606461, #30606467, … |
| maximal normal subgroup of | #30606132, #30606461, #30606467, … |
| maximal quotient of | #30603680, #30603681, #30603691, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20722);