Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×Dic15 |
| unambiguous semidirect product | (C2×C3)⋊(C5×Dic5) |
| derived | C3×C5 ⋊ C2×C4×C5 |
| Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | D15 |
| commutator, hypocenter | C3×C5 | C2×C4×C5 |
| Frattini | C2 | C2×C5×D15 |
| Fitting, socle, prime radical | C22×C3×C52 | C2 |
| cosocle | C2×C3×C5 | C22×C5 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C22×C5 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C5×Dic3×Dic5, C5×#6665, C5×(C2×D3)⋊Dic5, … |
| maximal normal subgroup of | C5×Dic3×Dic5, C5×#6665, C5×(C2×D3)⋊Dic5, … |
| maximal quotient of | C2×C5×C3⋊#168, C5×#6710, C4×C5×Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 134);