Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C33×C9 |
| direct product | C37×#10624902 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C37 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C37 |
| prime radical | C34×C37 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ G | |
644 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,5,4,7,14,12,18,25)(3,8,19,11,17,13,10,6,15)(9,21,26,22,16,27,23,20,24)(28,29,32)(30,33,39)(31,35,40)(34,44,38)(36,41,47)(37,43,48)(42,51,46)(45,50,53)(49,54,52)(55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91);(1,3,9)(2,6,16)(4,11,22)(5,13,24)(7,8,20)(10,23,12)(14,15,26)(17,21,18)(19,27,25)(28,30,36,31,37,45,38,46,52)(29,33,41,35,43,50,34,42,49)(32,39,47,40,48,53,44,51,54);(29,34,35)(32,40,44)(33,42,43)(39,48,51)(41,49,50)(47,53,54);(3,10,11)(6,17,8)(9,22,23)(13,19,15)(16,20,21)(24,26,27)4477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 462);