Finite Group DatabasebetaFinite Group Databasebeta| order | 14337 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9×C59 · Schur multiplier (H2) = C33 |
| direct product | C3×C59×C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C33×C59 | C32 |
| commutator | C3 | C32×C9×C59 |
| Frattini, cosocle | C32 | C33×C59 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C33×C59 ◁ G | |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 80 |
| transitive degree | μt(G) = 14337 |
A minimal faithful permutation representation — 3 generators on 80 points:
(1,2,3)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80);(5,7,10)(8,12,11)(13,14,16,15,17,19,18,20,21);(4,5,8,6,7,11,9,10,12)5841 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14337, 33);