Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C101 ⋊ #1767 |
292 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 3 generators on 117 points:
(1,2,5,10,19,32,49,43,26,13,4,7,14,23,36,53,68,60,39,22,9,16,27,40,57,72,83,75,56,35,18,29,44,61,76,87,94,86,71,52,31,46,64,79,90,97,100,93,82,67,48,65,80,91,98,101,99,96,89,78,63,45,62,77,88,95,92,85,74,59,42,28,41,58,73,84,81,70,55,38,25,15,24,37,54,69,66,51,34,21,12,6,11,20,33,50,47,30,17,8,3)(102,104,105,103)(111,114)(115,117);(2,4,3,6)(5,9,8,15)(7,13,12,11)(10,18,17,28)(14,22,21,24)(16,26,25,20)(19,31,30,45)(23,35,34,41)(27,39,38,37)(29,43,42,33)(32,48,47,65)(36,52,51,62)(40,56,55,58)(44,60,59,54)(46,49,63,50)(53,67,66,80)(57,71,70,77)(61,75,74,73)(64,68,78,69)(72,82,81,91)(76,86,85,88)(79,83,89,84)(87,93,92,98)(90,94,96,95)(97,100,99,101)(107,109)(110,111,112,115,113,114,116,117);(2,3)(4,6)(5,8)(7,12)(9,15)(10,17)(11,13)(14,21)(16,25)(18,28)(19,30)(20,26)(22,24)(23,34)(27,38)(29,42)(31,45)(32,47)(33,43)(35,41)(36,51)(37,39)(40,55)(44,59)(46,63)(48,65)(49,50)(52,62)(53,66)(54,60)(56,58)(57,70)(61,74)(64,78)(67,80)(68,69)(71,77)(72,81)(73,75)(76,85)(79,89)(82,91)(83,84)(86,88)(87,92)(90,96)(93,98)(94,95)(97,99)(100,101)(102,103,105,104)(106,107,108,109)Polycyclic presentation:
2^7,101|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,h^a=h^100,c^b=cg,h^b=h^10,h^f=h^100856 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20296);