Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C37 · Schur multiplier (H2) = C33 |
| direct product | C3×C37×#6861 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C37 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C37 |
| prime radical | C34×C37 | C32 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C37 ◁ C34×C37 ◁ G | |
284 conjugacy classes of subgroups.
| minimal degree | μ(G) = 94 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 3 generators on 94 points:
(1,2,3)(58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94);(4,5,8)(6,12,16)(7,11,17)(9,18,14)(10,21,15)(13,23,26)(19,29,30)(20,28,25)(22,27,24)(31,32,35,34,37,44,42,48,54)(33,38,49,41,36,45,40,47,43)(39,46,53,51,56,57,52,50,55);(4,6,13,7,14,24,15,25,30)(5,9,19,11,20,23,10,12,22)(8,16,26,17,18,27,21,28,29)(31,33,39)(32,36,46)(34,41,51)(35,43,53)(37,47,56)(38,50,48)(40,52,42)(44,49,57)(45,55,54)3885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 144);