Finite Group DatabasebetaFinite Group Databasebeta| order | 945 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×3−1+2 |
| unambiguous semidirect product | C9⋊(C3×C5×C7) |
| unambiguous semidirect product | (C5×C9)⋊(C3×C7) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C5×C7 | C32 |
| commutator, Frattini, cosocle | C3 | C32×C5×C7 |
| prime radical | C32×C5×C7 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C5×C7 ◁ G | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 315 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2,3,4,5)(6,7,8,9,10,11,12)(13,14,16,15,18,20,19,17,21);(14,17,18)(16,20,21)385 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(945, 11);