Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43 |
| direct product | C2×C42×#6923 |
| unambiguous semidirect product | D61⋊C43 |
| Fitting | C2×C42×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | #6923 |
| commutator, hypocenter | C61 | C2×C43 |
| Frattini | C22 | C23×#6923 |
| Fitting | C2×C42×C61 | C4 |
| socle | C23×C61 | C22×C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C42 | |
1272 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460646, #30596059, #30596066, … |
| maximal normal subgroup of | C2×#21460646, #30596059, #30596066, … |
| maximal quotient of | C43×#6923, C2×#95×#6923, C2×C4×(C2×#6923)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20935);