Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×Dic3×C25 |
| unambiguous semidirect product | (C2×C3)⋊(C4×C25) |
| derived, Sylow | C3 ⋊ C2×C4×C25 |
| Hall | C3×C25 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C25 | D3 |
| commutator, hypocenter | C3 | C2×C4×C25 |
| Frattini | C2×C5 | C2×C5×D3 |
| Fitting | C22×C3×C25 | C2 |
| socle, prime radical | C22×C3×C5 | C2×C5 |
| cosocle | C2×C3×C5 | C22×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C22×C25 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 600 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic3×Dic25, #11924816, #11924817, … |
| maximal normal subgroup of | Dic3×Dic25, #11924816, #11924817, … |
| maximal quotient of | C2×C3⋊C8×C25, C25×#208, C4×Dic3×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 23);