Finite Group DatabasebetaFinite Group Databasebeta| order | 24540 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#22551124 |
| Fitting, socle, derived, Hall | C3×C5×C409 ⋊ C4 |
| Hall | C5×C409 ⋊ Dic3 |
| Hall | C3×C409 ⋊ AGL(1,𝔽5) |
| Sylow | C409 ⋊ ΓL(1,𝔽16) |
| Hall | C3×C5 ⋊ #13109888 |
| Sylow | C5 ⋊ C3⋊#13109888 |
| Sylow | C3 ⋊ #22551124 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C409 | C4 |
| prime radical, cosocle | C3×D2045 | C2 |
| LCS | G ▷ C3×C5×C409 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6135 |
Polycyclic presentation:
2^2,3,5,409|a^2=b,c^a=c^2,d^a=d^2,e^a=e^266,d^b=d^4,e^b=e^4081539 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24540, 34);