Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C22×D75 |
| Fitting | C22×C3×C25 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C23 |
| Sylow | C25 ⋊ C22×D3 |
| Sylow | C3 ⋊ C22×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C23 |
| Frattini | C5 | C22×D15 |
| Fitting | C22×C3×C25 | C2 |
| socle | C22×C3×C5 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C22 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | #11924820, #11924865, C2×#10597028, … |
| maximal normal subgroup of | #11924820, #11924865, C2×#10597028, … |
| maximal quotient of | C2×Dic150, C2×C4×D75, C2×D300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 43);