Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#6016 |
| derived, Hall | C3×C25 ⋊ C8 |
| Sylow | C25 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #6016 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C8 |
| Frattini | C2×C5 | ΓL(1,𝔽16) |
| Fitting | C2×C3×C25 | C4 |
| socle, prime radical | C2×C3×C5 | AGL(1,𝔽5) |
| cosocle | C3×Dic25 | C2 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^3,3,5^2|a^2=b,b^2=c,e^5=f,d^a=d^2,e^a=e^3f^3,f^a=f^3,e^b=e^4f^4,f^b=f^448 conjugacy classes — view the full character table.
| maximal subgroup of | #11924879, #11924880, D3×#6016, … |
| maximal normal subgroup of | #11924879, #11924880, D3×#6016, … |
| maximal quotient of | C3⋊#87709, C2×C3⋊#6016, C9⋊#6016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 6);