Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C37 · Schur multiplier (H2) = C32×C9 |
| direct product | C37×#10624550 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C33×C37 | C33 |
| commutator | C32 | C32×C9×C37 |
| Frattini, cosocle | C33 | C33×C37 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C37 ◁ G | |
374 conjugacy classes of subgroups.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 26973 |
A minimal faithful permutation representation — 3 generators on 64 points:
(2,6,8)(3,7,9)(11,12,16)(14,17,15)(19,20,22,21,23,25,24,26,27)(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);(1,2,7,5,8,9,4,6,3)(10,11,14,13,12,15,18,16,17);(1,3,6,4,9,8,5,7,2)(10,12,17,13,16,14,18,11,15)5661 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 110);