Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C22×C3×D25 |
| unambiguous semidirect product | C25⋊(C23×C3) |
| unambiguous semidirect product | (C2×C25)⋊(C22×C3) |
| Fitting | C22×C3×C25 ⋊ C2 |
| derived, Sylow | C25 ⋊ C23×C3 |
| Hall | C3×C25 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D25 |
| commutator, cosocle, hypocenter | C25 | C23×C3 |
| Frattini | C5 | C22×C3×D5 |
| Fitting | C22×C3×C25 | C2 |
| socle | C22×C3×C5 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C22×C3 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 300 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #11924819, C3×#87720, C3×C22⋊#1035, … |
| maximal normal subgroup of | #11924819, C3×#87720, C3×C22⋊#1035, … |
| maximal quotient of | C2×C3×Dic50, C2×C3×C4×D25, C2×C3×D100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 41);