Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C101 ⋊ #1417 |
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)(103,109)(105,122)(106,117)(107,129)(108,120)(110,136)(111,132)(112,141)(113,143)(114,134)(115,121)(116,125)(118,123)(119,127)(124,155)(126,157)(128,133)(130,148)(131,135)(137,149)(138,164)(139,163)(140,161)(142,165)(144,152)(145,154)(146,162)(147,160)(150,158)(151,153)(156,159);(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)(102,103,106,111,108,114,127,113)(104,115,117,144,120,145,119,151)(105,121,124,152,126,154,159,153)(107,128,123,112,130,140,158,142)(109,131,132,147,134,146,143,116)(110,135,137,160,139,162,138,125)(118,149,148,163,150,164,129,136)(122,141,155,161,157,165,156,133)Polycyclic presentation:
2^7,101|a^2=d,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,c^b=ce,e^b=ef,f^b=fg,h^d=h^100313 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19661);