Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C9 |
| direct product | C37×#10624540 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C37 | #6879 |
| commutator, Frattini, cosocle | C92 | C32×C37 |
| 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:
(1,2,6,5,10,23,18,33,22)(3,11,34,15,29,50,13,42,19)(4,9,20,17,30,21,47,66,53)(7,24,44,27,51,14,37,49,46)(8,28,64,31,54,16,32,52,39)(12,38,48,40,69,67,43,60,76)(25,58,79,61,78,81,68,80,72)(26,62,74,63,57,45,36,56,70)(35,55,41,65,77,71,59,75,73)(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);(1,3,12,39,70,79,17,46,71,5,15,40,64,74,81,47,44,73,18,13,43,16,45,72,4,14,41)(2,7,25,32,11,35,66,36,69,10,27,61,8,29,65,9,26,60,33,37,68,31,42,59,30,63,38)(6,19,48,28,56,78,21,49,75,23,34,67,54,62,80,53,24,55,22,50,76,52,57,58,20,51,77)1517 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 100);