Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C101 ⋊ #2245 |
132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 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) = 12928 |
A minimal faithful permutation representation — 3 generators on 141 points:
(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)(103,107)(106,109)(110,113,114,128,130,140,124,127,117,129,131,126,116,125,115,112)(111,119,120,137,132,141,133,136,123,138,139,135,122,134,121,118);(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)(103,106,107,109)(110,112,124,140,116,126,114,113,117,127,115,125,130,128,131,129)(111,118,133,141,122,135,120,119,123,136,121,134,132,137,139,138);(102,103)(104,106)(105,107)(108,109)(110,111,117,123)(112,119,127,138)(113,118,129,136)(114,121,131,133)(115,120,124,139)(116,132,130,122)(125,137,140,135)(126,141,128,134)Polycyclic presentation:
2^7,101|a^2=g,b^2=eg,c^2=d,d^2=fg,e^2=f,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,c^b=cg,h^c=h^1001126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 6754);