Finite Group DatabasebetaFinite Group Databasebeta| order | 23940 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊(C7⋊AGL(1,𝔽5)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C19 | C4×C9 |
| prime radical, cosocle | C7×D5×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 665 |
Polycyclic presentation:
2,3,2,3,5,7,19|a^2=c,b^3=d,e^a=e^2,f^a=f^6,g^a=g^18,g^b=g^4,e^c=e^4,g^d=g^7181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23940, 328);