Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C101 ⋊ #1287 |
126 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 2 generators on 133 points:
(1,2,8,4)(3,6,18,14)(5,7,16,10)(9,12,32,24)(11,17,28,20)(13,15,30,26)(19,22,50,38)(21,31,42,34)(23,25,48,44)(27,29,46,40)(33,36,51,54)(35,49,58,52)(37,39,68,60)(41,47,64,56)(43,45,66,62)(53,69,72,55)(57,67,76,70)(59,61,82,78)(63,65,80,74)(71,83,86,73)(75,81,90,84)(77,79,92,88)(85,93,96,87)(89,91,98,94)(95,99,100,97)(102,104,106,113,107,114,105,115)(103,108,111,116,109,112,110,117)(118,120)(119,123,125,130)(121,127)(122,128)(124,126,131,132)(129,133);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,54,50)(42,49,57,56)(45,59,60,48)(46,47,63,62)(58,69,71,70)(61,73,72,68)(64,67,75,74)(65,77,78,66)(76,83,85,84)(79,87,86,82)(80,81,89,88)(90,93,95,94)(91,97,96,92)(98,99,101,100)(102,103,105,110,107,109,106,111)(104,112,113,117,114,108,115,116)(118,119)(120,126,128,132)(121,124)(122,125)(123,127,130,133)(129,131)Polycyclic presentation:
2^7,101|a^2=d,b^2=e,c^2=fg,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^91,d^b=dg,h^b=h^10,h^d=h^100,h^e=h^100532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 19368);