Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C32 |
| direct product | C37×#10624478 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C37 | #6856 |
| commutator, Frattini, cosocle | C32×C9 | C32×C37 |
| prime radical | C3×C37×#732 | C3 |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C37 ◁ C33×C37 ◁ C32×C9×C37 ◁ G | |
122 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 2 generators on 118 points:
(1,2,6,5,10,23,20,9,32)(3,11,33,15,36,68,14,29,58)(4,16,22,19,8,28,51,31,65)(7,24,49,27,59,47,26,55,42)(12,37,72,39,71,57,44,73,80)(13,40,21,43,35,53,17,46,54)(18,48,56,50,45,64,78,30,66)(25,60,76,63,81,38,62,67,41)(34,69,75,70,52,77,61,79,74)(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)(2,7,25)(4,17,38)(5,15,39)(6,21,52)(8,29,61)(9,26,62)(10,27,63)(11,34,31)(13,41,19)(14,44,20)(16,36,70)(18,49,74)(22,55,72)(23,53,79)(24,57,28)(30,46,73)(32,54,69)(33,67,56)(35,71,45)(37,48,40)(42,77,78)(43,76,51)(47,75,50)(58,81,66)(59,80,65)(60,64,68)1517 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 38);