Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of C3⋊#1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊#1043 |
| unambiguous semidirect product | (C2×C3)⋊#1043 |
| Fitting, socle | C2×C3×C52 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C2×Dic3 |
| Sylow | C3 ⋊ C2×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊#1043 |
| commutator, hypocenter | C3×C52 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52 | C4 |
| prime radical | C2×C3×C5⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C22 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 150 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | Dic3×#1043, (C2×D3)⋊#1043, Dic3⋊#1043, … |
| maximal normal subgroup of | Dic3×#1043, (C2×D3)⋊#1043, Dic3⋊#1043, … |
| maximal quotient of | #11925527, #11925528, C4×C3⋊#1043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 189);