Finite Group DatabasebetaFinite Group Databasebeta| order | 3900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D13×D25 |
| Fitting, Hall | C3×C13×C25 ⋊ C22 |
| derived, Hall | C13×C25 ⋊ C22×C3 |
| Hall | C3×C25 ⋊ C2×D13 |
| Hall | C3×C13 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×C3×D13 |
| Sylow | C13 ⋊ C2×C3×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D13×D25 |
| commutator, cosocle, hypocenter | C13×C25 | C22×C3 |
| Frattini | C5 | C3×D5×D13 |
| Fitting | C3×C13×C25 | C22 |
| socle | C3×C5×C13 | C2×D5 |
| LCS | G ▷ C13×C25 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 975 |
336 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D25×D13⋊C9, C9×D13×D25, C3×D25×D13⋊C3, … |
| maximal normal subgroup of | D25×D13⋊C9, C9×D13×D25, C3×D25×D13⋊C3, … |
| maximal quotient of | C9×D13×D25, C32×D13×D25, C3×D13×D75, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3900, 36);