Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C101 ⋊ #1401 |
72 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)(103,110)(105,121)(106,124)(107,119)(108,117)(109,120)(111,134)(112,137)(113,132)(114,116)(115,133)(118,127)(122,145)(123,149)(125,152)(126,130)(128,146)(129,148)(131,140)(135,143)(136,158)(138,160)(139,151)(141,144)(142,157)(147,154)(150,164)(153,155)(156,162)(159,163)(161,165);(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)(102,103,106,112,107,113,125,138,108,114,126,139,128,141,153,161,109,115,127,140,129,142,154,162,105,111,122,135,123,136,150,159)(104,116,118,143,119,144,147,163,117,133,145,137,146,157,164,160,120,134,124,151,148,158,152,165,121,110,130,131,149,132,155,156)Polycyclic presentation:
2^7,101|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^10,c^b=cg,d^b=dg,h^d=h^100556 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19627);