Finite Group DatabasebetaFinite Group Databasebeta| order | 3900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C13⋊C3×D25 |
| unambiguous semidirect product | C25⋊(C22×C13⋊C3) |
| unambiguous semidirect product | (C2×C25)⋊(C2×C13⋊C3) |
| unambiguous semidirect product | (C2×C13×D25)⋊C3 |
| Fitting | C2×C13×C25 ⋊ C2×C3 |
| derived, Hall | C13×C25 ⋊ C22×C3 |
| Hall | C2×C13×D25 ⋊ C3 |
| Hall | C25×C13⋊C3 ⋊ C22 |
| Sylow | C25 ⋊ C22×C13⋊C3 |
| Sylow | C13 ⋊ C2×C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C13⋊C3×D25 |
| commutator, cosocle, hypocenter | C13×C25 | C22×C3 |
| Frattini | C5 | C2×D5×C13⋊C3 |
| Fitting | C2×C13×C25 | C2×C3 |
| socle | C2×C5×C13 | C3×D5 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 650 |
196 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C13⋊C3×D25, C2×C3×C13⋊C3×D25, C2×C13⋊C3×D75, … |
| maximal normal subgroup of | C2×C3×C13⋊C3×D25, C2×C7×C13⋊C3×D25 |
| maximal quotient of | C2×D25×C13⋊C9, D3×C13⋊C3×D25, C2×C3×C13⋊C3×D25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3900, 22);