Finite Group DatabasebetaFinite Group Databasebeta| order | 31740 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting, socle, Hall | C5×C232 ⋊ Dic3 |
| derived, Hall | C5×C232⋊C3 ⋊ C4 |
| Hall | C232⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C232 ⋊ ΓL(1,𝔽16) |
| Sylow | C5 ⋊ #20263661 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C5×C232⋊C3 | C4 |
| Fitting, socle | C5×C232 | Dic3 |
| prime radical, cosocle | C5⋊((C23⋊D23)⋊C3) | C2 |
| LCS | G ▷ C5×C232⋊C3 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
Polycyclic presentation:
2^2,3,5,23^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^7f^18,f^a=e^10f^16,d^b=d^4,e^b=e^22,f^b=f^22,e^c=e^7f^3,f^c=e^4f^15229 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 54);