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 58 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 58 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:
(1,2,8,5)(3,6,18,14)(4,7,16,11)(9,12,32,24)(10,17,28,21)(13,15,30,27)(19,22,50,38)(20,31,42,35)(23,25,48,44)(26,29,46,41)(33,36,51,54)(34,49,58,53)(37,39,68,60)(40,47,64,57)(43,45,66,63)(52,69,72,55)(56,67,76,71)(59,61,82,78)(62,65,80,75)(70,83,86,73)(74,81,90,85)(77,79,92,89)(84,93,96,87)(88,91,98,95)(94,99,101,97)(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);(2,4)(3,5)(6,10)(7,14)(8,13)(9,11)(12,20)(15,24)(16,26)(17,27)(18,23)(19,21)(22,34)(25,38)(28,40)(29,44)(30,43)(31,41)(32,37)(33,35)(36,52)(39,54)(42,56)(45,60)(46,62)(47,63)(48,59)(49,57)(50,55)(51,53)(58,70)(61,72)(64,74)(65,78)(66,77)(67,75)(68,73)(69,71)(76,84)(79,86)(80,88)(81,89)(82,87)(83,85)(90,94)(91,96)(92,97)(93,95)(98,100)(99,101)(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);(2,3,4,5)(6,9,10,11)(7,13,14,8)(12,19,20,21)(15,23,24,18)(16,17,26,27)(22,33,34,35)(25,37,38,32)(28,31,40,41)(29,43,44,30)(36,51,52,53)(39,55,54,50)(42,49,56,57)(45,59,60,48)(46,47,62,63)(58,69,70,71)(61,73,72,68)(64,67,74,75)(65,77,78,66)(76,83,84,85)(79,87,86,82)(80,81,88,89)(90,93,94,95)(91,97,96,92)(98,99,100,101)(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^91,d^b=dg,h^b=h^100,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, 20899);