Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C37 · Schur multiplier (H2) = C32 |
| direct product | C37×#10624471 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C37 | C9⋊C9 |
| commutator | C9 | C92×C37 |
| Frattini, cosocle | C32×C9 | C32×C37 |
| socle | C3×C37 | #6855 |
| prime radical | C33×C37 | 3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C37 ◁ C32×C9×C37 ◁ G | |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 2 generators on 118 points:
(1,2,7,5,10,25,19,35,24,6,11,27,21,36,58,51,9,32,22,33,26,18,50,60,4,17,49)(3,12,37,15,31,64,48,34,57,16,39,59,20,52,63,14,44,56,45,69,62,54,8,28,46,30,23)(13,40,72,42,38,55,41,29,65,43,66,81,47,71,79,74,67,70,75,68,61,53,77,78,76,73,80)(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);(1,3,13)(2,8,29,11,31,67,33,52,73)(4,14,41)(5,20,53)(6,16,43)(7,23,55,26,56,78,27,57,79)(9,12,38,17,39,71,35,69,77)(10,34,40,36,44,66,50,30,68)(15,47,18)(19,46,74)(21,54,42)(22,45,75)(24,28,61,49,63,81,32,64,72)(25,59,80,60,37,70,58,62,65)(48,76,51)3885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 31);