Finite Group DatabasebetaFinite Group Databasebeta| order | 12879 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C53 · Schur multiplier (H2) = C3 |
| direct product | C53×#6899 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C53 |
| prime radical | C33×C53 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ G | |
110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 4293 |
A minimal faithful permutation representation — 3 generators on 89 points:
(2,5,3)(6,7,8)(10,11,14)(12,15,21)(13,17,22)(16,26,20)(18,23,29)(19,25,30)(24,33,28)(27,32,35)(31,36,34)(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);(1,2,6,9,3,7,4,5,8)(10,12,18,13,19,27,20,28,34)(11,15,23,17,25,32,16,24,31)(14,21,29,22,30,35,26,33,36);(1,3,8,9,5,6,4,2,7)(11,16,17)(14,22,26)(15,24,25)(21,30,33)(23,31,32)(29,35,36)2703 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12879, 46);