Finite Group DatabasebetaFinite Group Databasebeta| order | 20295 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C41 · Schur multiplier (H2) = C3 |
| direct product | C32×C41×C11⋊C5 |
| unambiguous semidirect product | C11⋊(C32×C5×C41) |
| unambiguous semidirect product | (C3×C11)⋊(C3×C5×C41) |
| unambiguous semidirect product | (C32×C11)⋊(C5×C41) |
| Fitting, socle, Hall | C32×C11×C41 ⋊ C5 |
| derived, Sylow | C11 ⋊ C32×C5×C41 |
| Hall | C11×C41 ⋊ C32×C5 |
| Hall | C32×C11 ⋊ C5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C41 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C32×C5×C41 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C41 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C32×C41 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4059 |
2583 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20295, 10);