Finite Group DatabasebetaFinite Group Databasebeta| order | 12416 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C97 ⋊ M128 |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 161 |
| transitive degree | μt(G) = 6208 |
A minimal faithful permutation representation — 2 generators on 161 points:
(1,2,6,15,31,58,82,93,78,63,69,41,66,85,46,74,71,24,50,72,54,25,4,11,27,43,70,89,59,84,61,12,21,8,18,39,65,90,96,67,92,87,37,52,13,29,35,16,32,40,7,17,36,28,53,34,60,88,91,95,97,81,55,33,3,9,22,45,73,38,62,68,20,44,26,10,23,47,75,79,49,51,80,48,76,77,19,42,56,83,94,64,86,57,30,14,5)(99,105)(106,120)(107,121)(108,122)(109,123)(124,140)(125,141)(126,142)(127,143)(128,144)(129,145)(146,155)(147,156)(148,157)(149,158)(159,161);(2,3,4,7,5,8,10,16)(6,12,13,15,14,22,28,30)(9,19,20,40,21,41,43,32)(11,24,25,48,26,49,23,46)(17,33,34,59,35,18,37,38)(27,51,52,65,44,71,53,81)(29,45,54,72,36,61,47,75)(31,55,56,82,57,39,63,64)(42,67,68,80,69,91,70,74)(50,77,78,89,79,66,83,62)(58,84,85,60,86,73,76,87)(88,95,94,90,92,96,93,97)(98,99,100,106,101,107,110,124,102,108,111,125,114,127,130,146,103,109,112,126,115,128,131,147,117,129,133,148,136,149,150,159,104,105,113,120,116,121,132,140,118,122,134,141,137,143,151,155,119,123,135,142,138,144,152,156,139,145,153,157,154,158,160,161)Polycyclic presentation:
2^7,97|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^64,h^c=h^22,h^d=h^96272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12416, 21614);