Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C9×C37 · Schur multiplier (H2) = C35 |
| direct product | C32×C37×C27⋊C3 |
| unambiguous semidirect product | C27⋊(C33×C37) |
| subgroup | G/H | |
|---|---|---|
| center | C32×C9×C37 | C32 |
| commutator | C3 | C33×C9×C37 |
| Frattini, cosocle | C9 | C34×C37 |
| socle | C33×C37 | C3×C9 |
| prime radical | C34×C37 | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C9×C37 ◁ G | |
944 conjugacy classes of subgroups.
| minimal degree | μ(G) = 70 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 4 generators on 70 points:
(1,2,3)(34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(4,5,6);(7,8,11,9,13,19,15,22,27,10,14,18,16,23,26,24,30,32,17,12,20,25,21,28,31,29,33);(8,12,14)(11,18,20)(13,21,23)(19,26,28)(22,29,30)(27,32,33)10989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 476);