Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊Dic35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(#4296⋊D7) |
| commutator, hypocenter | C5×C7×C19 | C4×C9 |
| Fitting, socle | C2×C5×C7×C19 | C2×C9 |
| prime radical, cosocle | C2×C5×C7×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2660 |
Polycyclic presentation:
2,3^2,5,7,19,2|a^2=g,b^3=c,d^a=d^4,e^a=e^6,f^a=f^18,f^b=f^4,f^c=f^7412 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 216);