Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C101 ⋊ #1356 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 3232 |
A minimal faithful permutation representation — 2 generators on 133 points:
(1,2)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,60)(31,32)(34,56)(35,36)(38,52)(39,40)(42,50)(43,44)(45,46)(48,49)(51,75)(53,71)(54,55)(57,67)(58,59)(61,66)(62,63)(64,65)(68,86)(69,70)(72,82)(73,74)(76,81)(77,78)(79,80)(83,93)(84,85)(87,92)(88,89)(90,91)(94,99)(95,96)(97,98)(100,101)(102,104,107,116)(103,108,112,125)(105,117,118,122)(106,120,121,115)(109,124,111,113)(110,128,130,131)(114,119,132,126)(123,127,133,129);(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)(32,47,48,64)(36,51,49,60)(40,53,54,56)(44,57,58,52)(46,61,62,50)(55,68,69,75)(59,72,73,71)(63,76,77,67)(65,70,79,66)(74,83,84,86)(78,87,88,82)(80,85,90,81)(89,94,95,93)(91,96,97,92)(98,100,101,99)(102,103,105,110,106,111,119,129,107,112,118,130,121,109,126,127)(104,113,114,131,115,108,122,123,116,124,132,128,120,125,117,133)Polycyclic presentation:
2^7,101|a^2=d,b^2=g,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,h^a=h^91,c^b=cf,d^b=defg,e^b=eg,h^b=h^100,d^c=dg,h^d=h^100370 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19517);