Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C34 |
| direct product | C37×#10624914 |
| 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 | |
578 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 4 generators on 91 points:
(1,2,5)(3,7,14)(4,9,15)(6,13,8)(10,16,23)(11,18,24)(12,19,17)(20,25,27)(21,26,22)(28,29,32,31,35,41,39,34,45)(30,33,40,38,43,49,37,44,52)(36,42,48,46,51,54,47,50,53)(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)(3,10,14)(4,9,5)(7,17,12)(8,15,13)(11,21,26)(16,23,19)(18,24,27)(20,25,22)(28,30,36)(29,33,42)(31,38,46)(32,40,48)(34,44,50)(35,43,51)(37,47,39)(41,49,54)(45,52,53);(1,3,11,4,12,22,13,23,27)(2,7,18,9,19,21,8,10,20)(5,14,24,15,17,26,6,16,25)(29,34,35)(30,37,38)(32,41,45)(33,43,44)(36,46,47)(48,53,54);(2,8,9)(5,15,6)(7,10,19)(14,17,16)(18,20,21)(24,26,25)(29,34,35)(32,41,45)(33,44,43)(40,49,52)(42,50,51)(48,54,53)3293 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 474);