Finite Group DatabasebetaFinite Group Databasebeta| order | 8394 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D1399⋊C3 |
| unambiguous semidirect product | (C1399⋊C3)⋊C2 |
| Fitting, socle, derived, Sylow | C1399 ⋊ C2×C3 |
| Hall | C1399⋊C3 ⋊ C2 |
| Hall | D1399 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C1399 | C2×C3 |
| LCS | G ▷ C1399 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,1399|c^a=c^1398,c^b=c^1008239 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D1399⋊C3, C3×D1399⋊C3, C3⋊(D1399⋊C3) |
| maximal normal subgroup of | C2×D1399⋊C3, C3×D1399⋊C3 |
| maximal quotient of | (C1399⋊C3)⋊C4, C2×D1399⋊C3, D1399⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8394, 1);