Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C37 · Schur multiplier (H2) = C34 |
| direct product | C37×#10624900 |
| 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 | |
730 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 4 generators on 73 points:
(1,2,4,3,6,8,7,5,9)(11,14,17)(15,23,21)(16,22,26)(24,31,29)(25,30,33)(32,36,35)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(10,11,15)(12,16,24)(13,14,21)(17,23,20)(18,25,32)(19,22,29)(26,31,28)(27,30,35)(33,36,34);(2,5,6)(4,8,9)(10,12,18,13,19,27,20,28,34)(11,16,25,14,22,30,17,26,33)(15,24,32,21,29,35,23,31,36);(11,17,14)(15,21,23)(16,26,22)(24,29,31)(25,33,30)(32,35,36)4477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 460);