Finite Group DatabasebetaFinite Group Databasebeta| order | 21460 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D5×C29×D37 |
| unambiguous semidirect product | (D5×C37)⋊(C2×C29) |
| unambiguous semidirect product | (C5×D37)⋊(C2×C29) |
| unambiguous semidirect product | D185⋊(C2×C29) |
| Fitting, socle, Hall | C5×C29×C37 ⋊ C22 |
| derived, Hall | C5×C37 ⋊ C22×C29 |
| Hall | C29×C37 ⋊ C2×D5 |
| Hall | C5×C29 ⋊ C2×D37 |
| Sylow | C37 ⋊ C2×D5×C29 |
| Sylow | C5 ⋊ C2×C29×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D5×D37 |
| commutator, cosocle, hypocenter | C5×C37 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C5×C29×C37 | C22 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C29 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5365 |
2320 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21460, 34);