Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C9 |
| direct product | C37×#10624536 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C37 | #6879 |
| commutator, Frattini, cosocle | C92 | C32×C37 |
| prime radical | C32×C37 | #732 |
| LCS | G ▷ C92 ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C37 ◁ C32×C37 ◁ C3×C9×C37 ◁ C92×C37 ◁ G | |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 2 generators on 118 points:
(1,2,6,5,10,22,17,31,21)(3,11,18,14,34,46,41,57,45)(4,9,19,16,28,20,42,60,48)(7,23,40,26,44,68,58,53,13)(8,27,59,29,49,15,30,47,36)(12,35,43,38,63,71,67,55,70)(24,54,76,56,73,81,79,77,65)(25,51,64,33,52,75,62,72,39)(32,50,66,61,69,80,78,74,37)(82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118);(1,3,12,36,64,76,16,40,66,5,14,38,59,75,81,42,68,80,17,41,67,15,39,65,4,13,37)(2,7,24,30,57,78,60,62,63,10,26,56,8,11,32,9,25,55,31,58,79,29,34,61,28,33,35)(6,18,43,27,52,73,20,44,69,22,46,71,49,72,77,48,53,74,21,45,70,47,51,54,19,23,50)3293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 96);