Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| isoclinism | isoclinic class of #6923 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×#6923 |
| unambiguous semidirect product | D61⋊(C22×C42) |
| Fitting | C23×C4×C61 ⋊ C4 |
| derived, Sylow | C61 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | #6923 |
| commutator, hypocenter | C61 | C23×C42 |
| Frattini | C2 | C24×#6923 |
| Fitting | C23×C4×C61 | C4 |
| socle | C24×C61 | C2×C4 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C23×C4 | |
3000 conjugacy classes of subgroups.
608 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#6923)⋊#95, #30602344, #30602368, … |
| maximal normal subgroup of | (C2×#6923)⋊#95, #30602344, #30602368, … |
| maximal quotient of | C22×C42×#6923, C23×(C2×#6923)⋊C4, C22×#16840698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21480);