Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C37 · Schur multiplier (H2) = C33 |
| direct product | C37×#10624771 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C37 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C37 |
| prime radical | C34×C37 | C32 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C37 ◁ C34×C37 ◁ G | |
356 conjugacy classes of subgroups.
| minimal degree | μ(G) = 73 |
| transitive degree | μt(G) = 2997 |
A minimal faithful permutation representation — 3 generators on 73 points:
(1,2,4,3,6,8,7,5,9)(10,11,14)(12,18,22)(13,17,23)(15,24,19)(16,27,21)(20,31,33)(25,34,29)(26,36,32)(28,35,30)(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);(2,5,6)(4,8,9)(12,19,29)(15,25,18)(20,32,30)(22,24,34)(26,28,31)(33,36,35);(10,12,20,13,19,30,21,29,32)(11,15,26,17,25,31,16,18,28)(14,22,33,23,24,35,27,34,36)2109 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 331);