Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#10624500 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C37 | C92 |
| commutator | C9 | C92×C37 |
| Frattini, cosocle | C3×C27 | C32×C37 |
| socle | C3×C37 | #6864 |
| prime radical | C32×C37 | C27⋊C3 |
| LCS | G ▷ C9 ▷ C1 | |
| UCS | C1 ◁ C9×C37 ◁ G | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 2 generators on 118 points:
(1,2,6,3,8,20,13,29,46,4,10,22,14,31,48,38,61,72,16,27,50,39,56,69,66,59,80,5,11,21,15,32,47,37,62,73,17,34,49,40,54,45,65,77,71,41,26,43,67,28,57,78,58,79,18,9,33,12,30,63,35,60,81,42,24,19,36,53,44,64,76,70,68,7,23,51,25,52,74,55,75)(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);(2,7,24,9,26,34,11,27,10)(3,12,15)(6,19,43,21,22,23,33,49,50)(8,28,31,30,56,53,32,25,54)(13,37,35)(14,36,40)(20,45,52,47,44,69,63,48,57)(29,59,77,60,55,61,62,58,76)(38,65,64)(39,51,67)(46,72,80,73,71,79,81,70,75)(66,78,74)3885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 60);