Finite Group DatabasebetaFinite Group Databasebeta| order | 21378 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D3563 |
| unambiguous semidirect product | C509⋊(C3×D7) |
| Fitting, socle, Hall | C3×C7×C509 ⋊ C2 |
| derived, Hall | C7×C509 ⋊ C2×C3 |
| Hall | C3×C509 ⋊ D7 |
| Sylow | C509 ⋊ C3×D7 |
| Hall | C3×C7 ⋊ D509 |
| Sylow | C7 ⋊ C3×D509 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3563 |
| commutator, cosocle, hypocenter | C7×C509 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C509 | C2 |
| LCS | G ▷ C7×C509 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10689 |
5349 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21378, 5);