Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C19 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×C19×C31⋊C3 |
| unambiguous semidirect product | (C22×C31⋊C3)⋊(C3×C19) |
| unambiguous semidirect product | (A4×C31)⋊(C3×C19) |
| unambiguous semidirect product | (C22⋊(C31⋊C3))⋊(C3×C19) |
| Fitting, socle, Hall | C22×C19×C31 ⋊ C32 |
| derived, Hall | C22×C31 ⋊ C32×C19 |
| Hall | C19×C31 ⋊ C3×A4 |
| Hall | C22×C19 ⋊ C3×C31⋊C3 |
| Sylow | C31 ⋊ C3×A4×C19 |
| Sylow | C22 ⋊ C3×C19×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | A4×C31⋊C3 |
| commutator, cosocle, hypocenter | C22×C31 | C32×C19 |
| Frattini | C1 | G |
| Fitting, socle | C22×C19×C31 | C32 |
| LCS | G ▷ C22×C31 | |
| UCS | C1 ◁ C19 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2356 |
988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 170);