Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | #131×#6923 |
| Fitting | #131×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C22×#6923 |
| commutator, socle | C2×C61 | C22×C42 |
| Frattini | C4 | C23×#6923 |
| Fitting | #131×C61 | C4 |
| hypercenter | #131 | #6923 |
| hypocenter | C61 | C4×#131 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ #131 | |
572 conjugacy classes of subgroups.
380 conjugacy classes — view the full character table.
| maximal subgroup of | #350×#6923, #30606412, #443×#6923, … |
| maximal normal subgroup of | #350×#6923, #30606412, #443×#6923, … |
| maximal quotient of | #131×#92420, #30609684, C8×#14519864, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21077);