Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3⋊D3×C71⋊C7 |
| unambiguous semidirect product | (C2×C3)⋊(D3×C71⋊C7) |
| unambiguous semidirect product | (C2×C3⋊D3×C71)⋊C7 |
| Fitting, socle | C2×C32×C71 ⋊ C2×C7 |
| derived, Hall | C32×C71 ⋊ C22×C7 |
| Hall | C32×C71⋊C7 ⋊ C22 |
| Hall | C2×C3⋊D3×C71 ⋊ C7 |
| Sylow | C71 ⋊ C2×C7×C3⋊D3 |
| Sylow | C32 ⋊ C22×C71⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊D3×C71⋊C7 |
| commutator, cosocle, hypocenter | C32×C71 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C71 | C2×C7 |
| LCS | G ▷ C32×C71 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1278 |
204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 84);