Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C101 ⋊ #3127 |
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 141 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 4 generators on 141 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(102,104,105,108)(103,107,106,109)(112,122)(116,120)(121,137)(123,139)(130,134)(131,135)(136,141)(138,140);(110,113,114,125)(111,117,118,132)(112,121,122,137)(115,129,127,126)(116,130,120,134)(119,133,128,124)(123,140,139,138)(131,136,135,141);(103,106)(107,109)(110,112)(111,116)(113,121)(114,122)(115,123)(117,130)(118,120)(119,131)(124,141)(125,137)(126,138)(127,139)(128,135)(129,140)(132,134)(133,136);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,107)(105,106)(108,109)(110,111,114,118)(112,120,122,116)(113,124,125,133)(115,128,127,119)(117,129,132,126)(121,136,137,141)(123,131,139,135)(130,138,134,140)Polycyclic presentation:
2^7,101|a^2=g,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^100,d^b=dg,f^c=fg1732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 14810);