Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×#41×C101 ⋊ C4 |
| Sylow | C101 ⋊ #2884 |
716 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 198 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 — 4 generators on 133 points:
(1,2,5,10,19,32,49,42,25,12,3,7,14,23,36,53,68,59,38,21,8,16,27,40,57,72,83,74,55,34,17,29,44,61,76,87,94,85,70,51,30,46,64,79,90,97,99,92,81,66,47,65,80,91,98,101,100,96,89,78,63,45,62,77,88,95,93,86,75,60,43,28,41,58,73,84,82,71,56,39,26,15,24,37,54,69,67,52,35,22,13,6,11,20,33,50,48,31,18,9,4)(102,106,107,119)(103,110,111,125)(104,114,115,131)(105,116,117,118)(108,121,112,127)(109,122,123,124)(113,128,129,130)(120,132,126,133);(102,105,107,117)(103,109,111,123)(104,113,115,129)(106,118,119,116)(108,120,112,126)(110,124,125,122)(114,130,131,128)(121,133,127,132);(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)(102,104)(103,108)(105,113)(106,114)(107,115)(109,120)(110,121)(111,112)(116,128)(117,129)(118,130)(119,131)(122,132)(123,126)(124,133)(125,127);(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)(104,112,115,108)(105,109)(106,110)(107,111)(113,126,129,120)(114,127,131,121)(116,122)(117,123)(118,124)(119,125)(128,133,130,132)Polycyclic presentation:
2^7,101|a^2=f,c^2=g,d^2=g,b^a=be,e^a=eg,h^a=h^10,f^b=fg,h^b=h^100,d^c=dg,h^f=h^100541 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 21112);