Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C33 |
| direct product | C37×#10624477 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C37 | #6856 |
| commutator, Frattini, cosocle | C32×C9 | C32×C37 |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C37 ◁ C33×C37 ◁ C32×C9×C37 ◁ G | |
134 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)(3,11,33)(4,16,22)(5,10,23)(7,24,42)(8,28,19)(9,32,20)(12,37,72)(13,40,21)(14,29,58)(15,36,68)(17,46,54)(18,48,56)(25,60,41)(26,55,47)(27,59,49)(30,66,78)(31,65,51)(34,69,74)(35,53,43)(38,62,67)(39,71,57)(44,73,80)(45,64,50)(52,75,70)(61,79,77)(63,81,76)(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, 37);