Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C4×C52×D3 |
| Fitting | C3×C4×C52 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C4×C52 |
| Hall | C3×C52 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C52 | D3 |
| commutator, hypocenter | C3 | C2×C4×C52 |
| Frattini | C2 | C2×C52×D3 |
| Fitting | C3×C4×C52 | C2 |
| socle | C2×C3×C52 | C22 |
| prime radical | C2×C52×D3 | C2 |
| cosocle | C2×C3 | C22×C52 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C4×C52 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×#168, C5×#6650, D3×#6029, … |
| maximal normal subgroup of | C5×D3×#168, C5×#6650, D3×#6029, … |
| maximal quotient of | C52×D3×C8, C52×ΓL(1,𝔽25), C4×C52×Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 127);