Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C37 · Schur multiplier (H2) = C3 |
| direct product | C37×#10624516 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C37 | #6867 |
| commutator | C3×C9 | C3×C9×C37 |
| Frattini, cosocle | C32×C9 | C32×C37 |
| prime radical | C33×C37 | 3−1+2 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C37 ◁ C3×C9×C37 ◁ C32×C9×C37 ◁ G | |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 999 |
A minimal faithful permutation representation — 2 generators on 64 points:
(1,2,6,4,8,17,15,23,26,5,10,19,14,21,27,12,22,25,16,9,24,3,11,18,13,7,20)(28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64);(2,7,21,9,22,8,10,23,11)(3,4,14)(6,17,25,19,27,20,24,18,26)(12,15,13)2109 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 76);