Finite Group DatabasebetaFinite Group Databasebeta| order | 38571 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#13131976 |
| Fitting, socle, Hall | C13×C23×C43 ⋊ C3 |
| derived, Hall | C13×C43 ⋊ C3×C23 |
| Hall | C23×C43 ⋊ C13⋊C3 |
| Hall | C13×C23 ⋊ C43⋊C3 |
| Sylow | C43 ⋊ C23×C13⋊C3 |
| Sylow | C13 ⋊ C23×C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #13131976 |
| commutator, cosocle, hypocenter | C13×C43 | C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C43 | C3 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 ◁ C23 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12857 |
4347 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(38571, 4);