Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C22⋊#19127101 |
| derived, Hall | C22×C19×C31 ⋊ C9 |
| Hall | C19×C31 ⋊ C22⋊C9 |
| Hall | C22×C31 ⋊ #4294 |
| Hall | C22×C19 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ C22⋊#4294 |
| Sylow | C19 ⋊ C22⋊(C31⋊C9) |
| Sylow | C22 ⋊ #19127101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C22⋊#13183714 |
| commutator, hypocenter | C22×C19×C31 | C9 |
| Fitting, socle, prime radical, cosocle | C22×C3×C19×C31 | C3 |
| LCS | G ▷ C22×C19×C31 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10602 |
Polycyclic presentation:
3,2^2,19,31,3|a^3=f,b^a=c,c^a=bc,d^a=d^7,e^a=e^52364 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 49);