Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD32×C101 ⋊ C4 |
| Sylow | C101 ⋊ #2178 |
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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:
(1,2,8,4)(3,6,18,14)(5,7,16,10)(9,12,32,24)(11,17,28,20)(13,15,30,26)(19,22,50,38)(21,31,42,34)(23,25,48,44)(27,29,46,40)(33,36,51,54)(35,49,58,52)(37,39,68,60)(41,47,64,56)(43,45,66,62)(53,69,72,55)(57,67,76,70)(59,61,82,78)(63,65,80,74)(71,83,86,73)(75,81,90,84)(77,79,92,88)(85,93,96,87)(89,91,98,94)(95,99,100,97)(102,105,107,119,108,120,123,106)(103,110,111,128,113,129,112,121)(104,115,116,124,118,132,117,122)(109,125,126,131,127,133,130,114);(102,104)(103,109)(105,115)(106,122)(107,116)(108,118)(110,125)(111,126)(112,130)(113,127)(114,121)(117,123)(119,124)(120,132)(128,131)(129,133);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,54,50)(42,49,57,56)(45,59,60,48)(46,47,63,62)(58,69,71,70)(61,73,72,68)(64,67,75,74)(65,77,78,66)(76,83,85,84)(79,87,86,82)(80,81,89,88)(90,93,95,94)(91,97,96,92)(98,99,101,100)(102,103,107,111,108,113,123,112)(104,114,116,125,118,131,117,133)(105,110,119,128,120,129,106,121)(109,124,126,132,127,122,130,115)Polycyclic presentation:
2^7,101|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^91,d^b=df,f^b=fg,h^c=h^10,h^e=h^100319 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 20910);