Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #24902421⋊C3 |
| Fitting, socle, derived, Hall | C5×C232 ⋊ C3×C4 |
| Hall | #24902421 ⋊ C3 |
| Hall | C5×C232⋊C3 ⋊ C4 |
| Hall | C232⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C232 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #14523747⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C232 | C3×C4 |
| prime radical | C5⋊((C23⋊D23)⋊C3) | C2 |
| cosocle | C5⋊(C23⋊D23) | C2×C3 |
| LCS | G ▷ C5×C232 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
Polycyclic presentation:
2,3,2,5,23^2|a^2=c,d^a=d^2,e^a=e^8f^16,f^a=e^6f^15,e^b=e^6f^13,f^b=e^2f^16,d^c=d^4,e^c=e^22,f^c=f^22235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 55);