Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C27×C37 · Schur multiplier (H2) = C3 |
| direct product | C37×#10624499 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C27×C37 | C32 |
| commutator | C3 | C9×C27×C37 |
| Frattini, cosocle | C3×C27 | C32×C37 |
| socle, prime radical | C32×C37 | C3×C27 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C27×C37 ◁ G | |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 26973 |
A minimal faithful permutation representation — 2 generators on 127 points:
(10,11,15,12,17,27,20,32,46,13,18,28,21,33,47,37,54,68,23,35,48,39,56,69,59,75,83,14,19,26,22,34,44,38,55,65,24,36,45,40,57,66,60,76,81,42,58,67,62,77,82,78,87,89,25,16,29,41,30,49,61,51,70,43,31,50,63,52,71,79,73,84,64,53,72,80,74,85,88,86,90)(91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127);(1,2,4,3,5,7,6,8,9)(11,16,19)(15,26,29)(17,30,34)(18,31,36)(27,44,49)(28,45,50)(32,51,55)(33,52,57)(35,53,58)(46,65,70)(47,66,71)(48,67,72)(54,73,76)(56,74,77)(68,81,84)(69,82,85)(75,86,87)(83,89,90)10989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 59);