Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊#66774 |
| unambiguous semidirect product | (C7⋊#66774)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊#66774 |
| commutator, hypocenter | C5×C7×C17 | C4×C9 |
| Fitting, socle | C3×C5×C7×C17 | C3×C4 |
| prime radical, cosocle | C3×C7×D5×C17 | C2×C3 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5355 |
Polycyclic presentation:
2,3,2,5,7,17,3|a^2=c,b^3=g,d^a=d^2,e^a=e^6,f^a=f^16,e^b=e^2,d^c=d^4537 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 32);