Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C3⋊#1035 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#1035 |
| unambiguous semidirect product | (C2×C3)⋊#1035 |
| unambiguous semidirect product | D25⋊Dic3 |
| Fitting | C2×C3×C25 ⋊ C4 |
| derived, Hall | C3×C25 ⋊ C2×C4 |
| Sylow | C25 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×#1035 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#1035 |
| commutator, hypocenter | C3×C25 | C2×C4 |
| Frattini | C5 | C2×ΓL(1,𝔽16) |
| Fitting | C2×C3×C25 | C4 |
| socle | C2×C3×C5 | AGL(1,𝔽5) |
| prime radical | C2×C3×D25 | C2 |
| cosocle | C3×D25 | C22 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#1035, Dic3⋊#1035, (C2×D3)⋊#1035, … |
| maximal normal subgroup of | Dic3×#1035, Dic3⋊#1035, (C2×D3)⋊#1035, … |
| maximal quotient of | D25⋊(C3⋊C8), #11924903, C4×C3⋊#1035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 38);