Finite Group DatabasebetaFinite Group Databasebeta| order | 12879 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C92×C53 · Schur multiplier (H2) = C3 |
| direct product | C53×#6864 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C53 | C32 |
| commutator | C3 | C92×C53 |
| Frattini, cosocle | C3×C9 | C32×C53 |
| socle, prime radical | C32×C53 | C3×C9 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C53 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 12879 |
A minimal faithful permutation representation — 2 generators on 89 points:
(10,11,14,12,16,22,18,25,30,13,17,21,19,26,29,27,33,35,20,15,23,28,24,31,34,32,36)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89);(1,2,4,3,5,7,6,8,9)(11,15,17)(14,21,23)(16,24,26)(22,29,31)(25,32,33)(30,35,36)5247 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12879, 11);