Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M32×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1379 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22⋊#6923 |
| commutator | C4×C61 | C4×C8 |
| Frattini | C2×C8 | C2×#6923 |
| Fitting | M32×C61 | C4 |
| socle | C2×C61 | #336 |
| hypercenter | M32 | #6923 |
| hypocenter | C61 | #1379 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ M32 | |
136 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 54 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,c^2=g,d^2=f,f^2=g,b^a=bc,h^a=h^50,c^b=cg,d^b=dg,h^b=h^11,h^d=h^60,h^e=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460875, #30606188, #30606377, … |
| maximal normal subgroup of | C2×#21460875, #30606188, #30606377, … |
| maximal quotient of | #30594189, #30594199, #30594209, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19566);