Finite Group DatabasebetaFinite Group Databasebeta| order | 23340 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#21441158 |
| Fitting, socle, Hall | C3×C5×C389 ⋊ C4 |
| derived, Hall | C5×C389 ⋊ C3×C4 |
| Hall | C3×C389 ⋊ Dic5 |
| Sylow | C389 ⋊ C3×Dic5 |
| Hall | C3×C5 ⋊ #13095555 |
| Sylow | C5 ⋊ C3×#13095555 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #21441158 |
| commutator, hypocenter | C5×C389 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C389 | C4 |
| prime radical | C3×C5×D389 | C2 |
| cosocle | C5×D389 | C2×C3 |
| LCS | G ▷ C5×C389 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5835 |
1479 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23340, 15);