Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C101 ⋊ #1425 |
50 conjugacy classes of subgroups.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 2 generators on 165 points:
(1,2,5,10,19,32,49,42,25,12,3,7,14,23,36,53,68,59,38,21,8,16,27,40,57,72,83,74,55,34,17,29,44,61,76,87,94,85,70,51,30,46,64,79,90,97,99,92,81,66,47,65,80,91,98,101,100,96,89,78,63,45,62,77,88,95,93,86,75,60,43,28,41,58,73,84,82,71,56,39,26,15,24,37,54,69,67,52,35,22,13,6,11,20,33,50,48,31,18,9,4)(102,104,116,143,107,119,124,131,106,118,135,159,127,149,126,148,109,121,145,164,129,151,125,147,108,120,144,163,123,146,105,117)(103,110,122,141,113,133,154,152,130,158,156,165,157,161,137,142,114,134,155,162,138,160,136,140,112,132,153,150,128,139,111,115);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,65)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,49,63,50)(53,66,67,80)(57,70,71,77)(61,74,75,73)(64,68,78,69)(72,81,82,91)(76,85,86,88)(79,83,89,84)(87,92,93,98)(90,94,96,95)(97,99,100,101)(102,103,106,112,109,114,108,130)(104,115,118,140,121,142,120,152)(105,122,124,153,126,155,125,156)(107,128,127,138,129,157,123,113)(110,131,132,148,134,147,158,117)(111,135,136,145,137,144,154,116)(119,150,149,162,151,165,146,141)(133,143,139,159,160,164,161,163)Polycyclic presentation:
2^7,101|a^2=d,b^2=ce,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^10,h^d=h^100838 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19673);