Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C101 ⋊ #2170 |
146 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 3232 |
A minimal faithful permutation representation — 3 generators on 133 points:
(1,2,7,3)(4,11,14,8)(5,16,12,6)(9,24,23,17)(10,29,25,15)(13,20,27,21)(18,41,36,30)(19,46,42,28)(22,37,40,34)(26,33,44,38)(31,62,53,47)(32,65,49,45)(35,58,57,51)(39,54,61,55)(43,50,64,59)(48,80,68,63)(52,77,72,66)(56,73,76,70)(60,69,79,74)(67,91,83,78)(71,88,87,81)(75,84,90,85)(82,98,94,89)(86,95,97,92)(93,101,99,96)(102,105,107,114,106,119,121,125,108,120,123,127,122,133,126,109)(103,104,111,116,112,117,129,131,113,118,130,132,110,115,128,124);(102,104)(103,109)(105,111)(106,117)(107,116)(108,118)(110,127)(112,114)(113,125)(115,122)(119,129)(120,130)(121,131)(123,132)(124,126)(128,133);(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)(102,103,107,111,106,112,121,129,108,113,123,130,122,110,126,128)(104,114,116,119,117,125,131,120,118,127,132,133,115,109,124,105)Polycyclic presentation:
2^7,101|a^2=e,c^2=e,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,h^a=h^10,d^b=dg,h^c=h^10,h^e=h^100406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20897);