Finite Group DatabasebetaFinite Group Databasebeta| order | 21420 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C7⋊C9)⋊Dic85 |
| unambiguous semidirect product | Dic595⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊(C17⋊AGL(1,𝔽7)) |
| commutator, hypocenter | C5×C7×C17 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C7×C17 | C2×C3 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 ◁ C2×C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 21420 |
Polycyclic presentation:
2,3,5,7,17,2,3|a^2=f,b^3=g,c^a=c^4,d^a=d^6,e^a=e^16,d^b=d^21302 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21420, 24);