Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D5×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic5×D15 |
| derived, Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D3 |
| Sylow | C3 ⋊ D5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D15 |
| commutator, hypocenter | C3×C52 | C2×C4 |
| Fitting, socle, cosocle | C2×C3×C52 | C22 |
| prime radical | C2×C5×D15 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
72 conjugacy classes — view the full character table.
| maximal subgroup of | D15×#170, #11925369, #11925381, … |
| maximal normal subgroup of | D15×#170, #11925369, #11925381, … |
| maximal quotient of | D15×#168, #11925127, Dic5×Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 99);