Finite Group DatabasebetaFinite Group Databasebeta| order | 21370 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2137 |
| unambiguous semidirect product | C2137⋊(C2×C5) |
| Fitting, socle, Hall | C5×C2137 ⋊ C2 |
| derived, Sylow | C2137 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2137 |
| commutator, cosocle, hypocenter | C2137 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C2137 | C2 |
| LCS | G ▷ C2137 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10685 |
5350 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21370, 2);