Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C37 · Schur multiplier (H2) = C32 |
| direct product | C37×#10624485 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C37 | #6857 |
| 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 | |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 118 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 2 generators on 118 points:
(1,2,6,5,10,22,19,9,31)(3,11,32)(4,8,21,18,30,53,48,29,64)(7,23,41)(12,36,69,43,72,54,38,70,79)(13,39,50)(14,35,66)(15,27,55)(16,44,51)(17,28,52,47,63,78,76,62,81)(20,42,34)(24,58,74,60,80,40,59,65,37)(25,56,45)(26,57,46)(33,67,73,68,77,71,61,49,75)(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);(1,3,12)(2,7,24)(4,16,37)(5,15,38)(6,20,49)(8,27,61)(9,25,60)(10,26,59)(11,33,29)(13,40,18)(14,43,19)(17,46,71)(21,23,54)(22,51,77)(28,39,72)(30,35,68)(31,50,67)(32,65,81)(34,36,63)(41,75,76)(42,74,48)(44,70,62)(45,73,47)(52,55,80)(53,57,69)(56,79,64)(58,78,66)1517 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 45);