Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | C7⋊C9×#66775 |
| unambiguous semidirect product | (C7×#66775)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)×#66775 |
| commutator, hypocenter | C5×C7×C17 | C4×C9 |
| Fitting, socle | C3×C5×C7×C17 | C3×C4 |
| prime radical, cosocle | C3×C7×D85 | C2×C3 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5355 |
375 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 34);