Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #473×C101 ⋊ C2 |
| Sylow | C101 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 165 |
| transitive degree | μt(G) = 6464 |
A minimal faithful permutation representation — 3 generators on 165 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)(102,105,109,124)(103,111,115,137)(104,117,120,149)(106,122,129,156)(107,130,108,123)(110,133,135,161)(112,136,140,153)(113,141,114,121)(116,143,144,164)(118,146,132,159)(119,148,131,147)(125,152,139,163)(126,154,157,165)(127,158,128,155)(134,160,142,151)(138,162,150,145);(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)(102,104)(103,110)(105,117)(106,126)(107,119)(108,131)(109,120)(111,133)(112,138)(113,134)(114,142)(115,135)(116,125)(118,128)(121,151)(122,154)(123,147)(124,149)(127,132)(129,157)(130,148)(136,162)(137,161)(139,144)(140,150)(141,160)(143,152)(145,153)(146,155)(156,165)(158,159)(163,164);(102,103,109,115)(104,116,120,144)(105,121,124,141)(106,125,129,139)(107,114,108,113)(110,132,135,118)(111,130,137,123)(112,127,140,128)(117,145,149,162)(119,150,131,138)(122,153,156,136)(126,142,157,134)(133,154,161,165)(143,148,164,147)(146,151,159,160)(152,158,163,155)Polycyclic presentation:
2^7,101|a^2=g,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,h^b=h^100,e^c=eg823 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 6486);