Finite Group DatabasebetaFinite Group Databasebeta| order | 19290 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D5×C643⋊C3 |
| unambiguous semidirect product | C5⋊(C2×C643⋊C3) |
| unambiguous semidirect product | (D5×C643)⋊C3 |
| Fitting, socle, derived, Hall | C5×C643 ⋊ C2×C3 |
| Hall | C5×C643⋊C3 ⋊ C2 |
| Hall | D5×C643 ⋊ C3 |
| Sylow | C643 ⋊ C3×D5 |
| Sylow | C5 ⋊ C2×C643⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C643 | C2×C3 |
| LCS | G ▷ C5×C643 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3215 |
868 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C643⋊C3)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C643⋊C3, D5×D643⋊C3, … |
| maximal normal subgroup of | (C643⋊C3)⋊AGL(1,𝔽5), AGL(1,𝔽5)×C643⋊C3, D5×D643⋊C3, … |
| maximal quotient of | Dic5×C643⋊C3, C2×D5×C643⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19290, 11);