Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C3⋊(C5⋊D5) |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#6029 |
| derived, Hall | C3×C52 ⋊ C8 |
| Sylow | C52 ⋊ C3⋊C8 |
| Sylow | C3 ⋊ #6029 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | C3⋊(C5⋊D5) |
| commutator, hypocenter | C3×C52 | C8 |
| Fitting, cosocle | C3×C4×C52 | C2 |
| socle, prime radical | C2×C3×C52 | C4 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C4 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
Polycyclic presentation:
2^3,3,5^2|a^2=b,b^2=c,d^a=d^2,e^a=e^4,f^a=f^4156 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊C8×C5⋊D5, D3×#6029, #11925102, … |
| maximal normal subgroup of | C3⋊C8×C5⋊D5, D3×#6029, #11925102, … |
| maximal quotient of | C3⋊#87756, C2×C3⋊#6029, C9⋊#6029, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 52);