Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #92420⋊C16 |
| Sylow | C61 ⋊ #1312 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×#6923 |
| commutator | C2×C61 | C4×C16 |
| Fitting | C2×C16×C61 | C4 |
| socle | C22×C61 | C4×C8 |
| hypercenter | C2×C16 | #6923 |
| hypocenter | C61 | #1312 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
92 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,b^a=be,h^a=h^11,h^c=h^60560 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#92420⋊C16, #30603685, #30603689, … |
| maximal normal subgroup of | C2×#92420⋊C16, #30603685, #30603689, … |
| maximal quotient of | #30594011, #30594176, #92420⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19424);