Finite Group DatabasebetaFinite Group Databasebeta| order | 3303 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C367⋊C9 |
| derived, Sylow | C367 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C367⋊C3 |
| commutator, hypocenter | C367 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C367 | C3 |
| LCS | G ▷ C367 | |
| UCS | C1 ◁ C3 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 376 |
| transitive degree | μt(G) = 3303 |
Polycyclic presentation:
3^2,367|a^3=b,c^a=c^283375 conjugacy classes — view the full character table.
| maximal subgroup of | C22⋊(C367⋊C9), C5×C367⋊C9, C7×C367⋊C9, … |
| maximal normal subgroup of | C5×C367⋊C9, C7×C367⋊C9, C11×C367⋊C9 |
| maximal quotient of | C22⋊(C367⋊C9), C5×C367⋊C9, C7×C367⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3303, 1);