Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C34 |
| direct product | C37×#10624907 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C37 | C34 |
| commutator, Frattini, cosocle | C32 | C34×C37 |
| prime radical | C3×H(3,𝔽3)×C37 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ G | |
622 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,5,8)(6,14,12)(7,13,17)(15,22,20)(16,21,24)(23,27,26)(28,29,32,31,35,40,38,34,44)(30,33,39,37,43,48,46,42,51)(36,41,47,45,50,53,52,49,54)(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);(1,2,6,4,5,12,11,8,14)(3,7,15,10,13,20,19,17,22)(9,16,23,18,21,26,25,24,27)(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);(1,3,9,4,10,18,11,19,25)(2,7,16,5,13,21,8,17,24)(6,15,23,12,20,26,14,22,27)(29,34,35)(32,40,44)(33,42,43)(39,48,51)(41,49,50)(47,53,54);(2,8,5)(6,12,14)(7,17,13)(15,20,22)(16,24,21)(23,26,27)4477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 467);