Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q32×C101 ⋊ C4 |
| Sylow | C101 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 44 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)(33,36,69,56)(34,49,52,53)(37,39,68,60)(40,47,64,58)(43,45,66,63)(51,54,67,71)(55,57,83,74)(59,61,82,78)(62,65,80,76)(70,72,81,85)(73,75,93,88)(77,79,92,90)(84,86,91,95)(87,89,99,97)(94,96,98,101)(102,105,107,106,108,119,124,121)(103,110,112,118,113,128,122,111)(104,115,123,120,116,132,117,133)(109,125,130,131,126,114,127,129);(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)(39,56)(42,54)(45,60)(46,62)(47,63)(48,59)(49,58)(50,55)(51,53)(57,71)(61,74)(64,72)(65,78)(66,77)(67,76)(68,73)(69,70)(75,85)(79,88)(80,86)(81,90)(82,87)(83,84)(89,95)(91,97)(92,96)(93,94)(98,101)(99,100)(102,104)(103,109)(105,115)(106,120)(107,123)(108,116)(110,125)(111,129)(112,130)(113,126)(114,128)(117,124)(118,131)(119,132)(121,133)(122,127);(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)(39,55,56,50)(42,49,54,58)(45,59,60,48)(46,47,62,63)(57,70,71,69)(61,73,74,68)(64,67,72,76)(65,77,78,66)(75,84,85,83)(79,87,88,82)(80,81,86,90)(89,94,95,93)(91,96,97,92)(98,100,101,99)(102,103)(104,114,116,125)(105,118)(106,110)(107,122)(108,113)(109,115,126,132)(111,119)(112,124)(117,129,123,131)(120,130,133,127)(121,128)Polycyclic presentation:
2^7,101|a^2=e,c^2=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^10,d^b=dfg,e^b=eg,f^b=fg,h^b=h^100,d^c=dg,h^c=h^91,h^e=h^100298 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20918);