Finite Group DatabasebetaFinite Group Databasebeta| order | 7839 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#14579732 |
| Fitting, socle | C3×C13×C67 ⋊ C3 |
| derived, Hall | C13×C67 ⋊ C32 |
| Sylow | C67 ⋊ C3×C13⋊C3 |
| Sylow | C13 ⋊ C3×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14579732 |
| commutator, hypocenter | C13×C67 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C67 | C3 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
879 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#19104951, C3×#19104947, C3×#19104943, … |
| maximal normal subgroup of | C3×#19104951, C3×#19104947, C3×#19104943, … |
| maximal quotient of | C2×C3×#14579732, A4×#14579732, C3×C22⋊#14579732 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7839, 9);