Finite Group DatabasebetaFinite Group Databasebeta| order | 21204 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C22×#19127102 |
| derived, Hall | C19×C31 ⋊ C22×C9 |
| Hall | C22×C19×C31 ⋊ C9 |
| Hall | C22×C31 ⋊ #4294 |
| Hall | C22×C19 ⋊ C31⋊C9 |
| Sylow | C31 ⋊ C22×#4294 |
| Sylow | C19 ⋊ C22×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #13183715 |
| commutator, hypocenter | C19×C31 | C22×C9 |
| Frattini | C3 | C22×#13183715 |
| Fitting, socle, prime radical | C22×C3×C19×C31 | C3 |
| cosocle | C3×C19×C31 | C22×C3 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C22×C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21204 |
2388 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21204, 55);