Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C101 ⋊ #1420 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 2 generators on 165 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,104,109,120)(103,110,114,136)(105,122,127,151)(106,119,108,117)(107,129,131,149)(111,138,141,147)(112,142,132,134)(113,143,144,145)(115,121,148,158)(116,125,152,162)(118,123,154,130)(124,160,126,159)(128,135,139,164)(133,137,150,161)(140,153,157,165)(146,163,155,156);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(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)(102,103,106,112,109,114,108,132)(104,115,117,146,120,148,119,155)(105,121,124,156,127,158,126,163)(107,128,123,144,131,139,130,113)(110,133,134,116,136,150,142,152)(111,137,140,162,141,161,157,125)(118,153,149,138,154,165,129,147)(122,143,159,164,151,145,160,135)Polycyclic presentation:
2^7,101|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^100,c^b=ceg,d^b=dg,e^b=ef,f^b=fg1126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 2703);