Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C101 ⋊ #1593 |
148 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 125 |
| transitive degree | μt(G) = 12928 |
A minimal faithful permutation representation — 3 generators on 125 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)(102,104,106,107,105,108,109,103)(111,116)(115,124)(117,121)(118,125);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,63)(47,65)(49,50)(51,62)(53,67)(54,59)(55,58)(57,71)(61,75)(64,78)(66,80)(68,69)(70,77)(72,82)(73,74)(76,86)(79,89)(81,91)(83,84)(85,88)(87,93)(90,96)(92,98)(94,95)(97,100)(99,101)(103,107)(104,108)(110,112,114,120)(111,115,116,124)(113,122,123,119)(117,125,121,118);(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)(102,103,106,104,105,107,109,108)(110,111)(112,118)(113,121)(114,116)(115,119)(117,123)(120,125)(122,124)Polycyclic presentation:
2^7,101|a^2=e,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cfg,d^a=df,h^a=h^10,c^b=cg,d^b=df,h^b=h^100,h^c=h^10,h^e=h^100382 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20156);