Finite Group DatabasebetaFinite Group Databasebeta| order | 21460 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#10625194 |
| Fitting, socle, Hall | C5×C29×C37 ⋊ C4 |
| derived, Hall | C5×C37 ⋊ C4×C29 |
| Hall | C29×C37 ⋊ Dic5 |
| Hall | C5×C29 ⋊ #3866 |
| Sylow | C37 ⋊ Dic5×C29 |
| Sylow | C5 ⋊ C29×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #10625194 |
| commutator, hypocenter | C5×C37 | C4×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C37 | C4 |
| prime radical | C5×C29×D37 | C2 |
| cosocle | C5×D37 | C2×C29 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C29 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5365 |
1537 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21460, 33);