Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C157 · Schur multiplier (H2) = C1 |
| direct product | M128×C157 |
| subgroup | G/H | |
|---|---|---|
| center | C32×C157 | C22 |
| commutator | C2 | C2×C32×C157 |
| Frattini, cosocle | C32 | C22×C157 |
| socle | C2×C157 | C2×C32 |
| prime radical | C22×C157 | C32 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C32×C157 ◁ G | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 2 generators on 221 points:
(1,2,3,9,4,10,13,27,5,11,14,28,17,30,33,49,6,12,15,29,18,31,34,50,20,32,36,51,39,52,53,62,7,8,16,23,19,24,35,43,21,25,37,44,40,46,54,58,22,26,38,45,41,47,55,59,42,48,56,60,57,61,63,64)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221);(2,8)(9,23)(10,24)(11,25)(12,26)(27,43)(28,44)(29,45)(30,46)(31,47)(32,48)(49,58)(50,59)(51,60)(52,61)(62,64)12560 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 160);