Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3×C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C5 |
| direct product | D3×#1039 |
| derived, Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D3 |
| Sylow | C3 ⋊ C2×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C5⋊D5 |
| commutator, hypocenter | C3×C52 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C52 | C22 |
| prime radical | C2×C52×D3 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#6033, #11925340, D3×#6034, … |
| maximal normal subgroup of | D3×#6033, #11925340, D3×#6034, … |
| maximal quotient of | D3×#6029, #11925103, Dic3×#1039, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 93);