Finite Group DatabasebetaFinite Group Databasebeta| order | 2673 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C11 · Schur multiplier (H2) = C35 |
| direct product | C32×C11×3−1+2 |
| unambiguous semidirect product | C9⋊(C33×C11) |
| unambiguous semidirect product | (C9×C11)⋊C33 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C11 | C32 |
| commutator, Frattini, cosocle | C3 | C34×C11 |
| prime radical | C34×C11 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C11 ◁ G | |
576 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 891 |
A minimal faithful permutation representation — 4 generators on 26 points:
(1,2,3)(16,17,18,19,20,21,22,23,24,25,26);(4,5,6);(7,8,10,9,12,14,13,11,15);(8,11,12)(10,14,15)1089 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2673, 63);