Finite Group DatabasebetaFinite Group Databasebeta| order | 30894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D271⋊C3 |
| unambiguous semidirect product | D271⋊(C3×C19) |
| unambiguous semidirect product | (C271⋊C3)⋊(C2×C19) |
| Fitting, socle, Hall | C19×C271 ⋊ C2×C3 |
| derived, Sylow | C271 ⋊ C2×C3×C19 |
| Hall | C19×C271⋊C3 ⋊ C2 |
| Hall | C19×D271 ⋊ C3 |
| Hall | C271⋊C3 ⋊ C2×C19 |
| Hall | D271 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D271⋊C3 |
| commutator, cosocle, hypocenter | C271 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C271 | C2×C3 |
| LCS | G ▷ C271 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5149 |
969 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30894, 13);