Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27×C37 · Schur multiplier (H2) = C34 |
| direct product | C3×C37×C32⋊C27 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C9×C37 | C32 |
| commutator | C3 | C32×C27×C37 |
| Frattini, cosocle | C3×C9 | C33×C37 |
| socle | C33×C37 | C3×C9 |
| prime radical | C34×C37 | C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C9×C37 ◁ G | |
464 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 8991 |
A minimal faithful permutation representation — 3 generators on 76 points:
(1,2,3)(40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76);(4,5,7)(6,9,11)(8,12,10)(13,14,17,15,18,23,20,25,30,16,19,24,21,26,31,28,33,36,22,27,32,29,34,37,35,38,39);(5,8,9)(7,11,12)10989 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 242);