Finite Group DatabasebetaFinite Group Databasebeta| order | 26973 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C35×C9 |
| abelian | C32×C92×C37 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C34×C37 |
| socle, prime radical | C34×C37 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2132 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 26973 |
A minimal faithful permutation representation — 4 generators on 61 points:
(1,2,3,4,5,6,7,8,9)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61);(10,11,12,13,14,15,16,17,18);(19,20,21);(22,23,24)26973 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26973, 415);