Finite Group DatabasebetaFinite Group Databasebeta| order | 20305 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C131 · Schur multiplier (H2) = C1 |
| direct product | C131×ΓL(1,𝔽32) |
| unambiguous semidirect product | C31⋊(C5×C131) |
| Fitting, socle, Hall | C31×C131 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C131 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C131 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C131 |
| Frattini | C1 | G |
| Fitting, socle | C31×C131 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C131 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4061 |
1441 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20305, 1);