Finite Group DatabasebetaFinite Group Databasebeta| order | 3681 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| direct product | C3×C409⋊C3 |
| unambiguous semidirect product | C409⋊C32 |
| unambiguous semidirect product | (C3×C409)⋊C3 |
| Fitting, socle | C3×C409 ⋊ C3 |
| derived, Sylow | C409 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C409⋊C3 |
| commutator, cosocle, hypocenter | C409 | C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C409 | C3 |
| LCS | G ▷ C409 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1227 |
417 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C409⋊C3, C32⋊(C409⋊C3), #26010702, … |
| maximal normal subgroup of | C9×C409⋊C3, C32⋊(C409⋊C3), #26010702, … |
| maximal quotient of | C9×C409⋊C3, C3×C409⋊C9, C32⋊(C409⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3681, 3);