Finite Group DatabasebetaFinite Group Databasebeta| order | 21810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C727⋊C3 |
| unambiguous semidirect product | (C2×C727)⋊(C3×C5) |
| unambiguous semidirect product | (C2×C5×C727)⋊C3 |
| Fitting, socle, Hall | C2×C5×C727 ⋊ C3 |
| derived, Sylow | C727 ⋊ C2×C3×C5 |
| Hall | C5×C727 ⋊ C2×C3 |
| Hall | C2×C727 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C727⋊C3 |
| commutator, cosocle, hypocenter | C727 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C727 | C3 |
| LCS | G ▷ C727 | |
| UCS | C1 ◁ C2×C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7270 |
2450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21810, 2);