Finite Group DatabasebetaFinite Group Databasebeta| order | 19197 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C79 · Schur multiplier (H2) = C3 |
| direct product | C79×#6900 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C79 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C79 |
| prime radical | C33×C79 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C79 ◁ G | |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 97 |
| transitive degree | μt(G) = 6399 |
A minimal faithful permutation representation — 3 generators on 97 points:
(2,4,7)(5,9,8)(11,13,16)(14,18,17)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(1,2,5,3,4,8,6,7,9);(10,11,14,12,13,17,15,16,18)4029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19197, 47);