Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C34 |
| direct product | C37×#10624908 |
| 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 | |
618 conjugacy classes of subgroups.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 4 generators on 91 points:
(2,6,15)(7,17,16)(8,11,22)(18,19,23)(20,21,24)(25,26,27)(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);(1,2,7)(3,8,18)(4,11,23)(5,6,16)(9,20,25)(10,21,27)(12,24,26)(13,22,19)(14,15,17)(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);(1,3,9,5,4,10,14,13,12)(2,8,20,6,11,21,15,22,24)(7,18,25,16,23,27,17,19,26)(29,34,35)(32,40,44)(33,42,43)(39,48,51)(41,49,50)(47,53,54);(1,4,12,5,13,9,14,3,10)(2,8,20,6,11,21,15,22,24)(7,19,27,16,18,26,17,23,25)4477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 468);