Finite Group DatabasebetaFinite Group Databasebeta| order | 21804 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D1817 |
| unambiguous semidirect product | (D3×C23)⋊D79 |
| unambiguous semidirect product | (D3×C79)⋊D23 |
| Fitting, socle, derived, Hall | C3×C23×C79 ⋊ C22 |
| Hall | C23×C79 ⋊ C2×D3 |
| Hall | C3×C79 ⋊ C2×D23 |
| Sylow | C79 ⋊ D3×D23 |
| Hall | C3×C23 ⋊ C2×D79 |
| Sylow | C23 ⋊ D3×D79 |
| Sylow | C3 ⋊ C2×D1817 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C23×C79 | C22 |
| LCS | G ▷ C3×C23×C79 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5451 |
2730 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21804, 23);