Finite Group DatabasebetaFinite Group Databasebeta| order | 12928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #504×C101 ⋊ C2 |
| Sylow | C101 ⋊ #3417 |
350 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 129 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 — 4 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)(105,119)(110,133)(115,143)(120,147)(121,148)(130,156)(134,158)(135,152)(141,163)(144,155)(145,153)(149,162)(150,165)(151,159)(157,161)(160,164);(102,105)(103,110)(104,115)(106,120)(107,121)(108,119)(109,130)(111,134)(112,135)(113,133)(114,141)(116,144)(117,145)(118,143)(122,149)(123,150)(124,148)(125,151)(126,147)(127,152)(128,153)(129,155)(131,157)(132,156)(136,159)(137,160)(138,158)(139,161)(140,162)(142,163)(146,164)(154,165);(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)(102,104,108,118)(103,109,113,132)(105,115,119,143)(106,123,126,154)(107,128,124,117)(110,130,133,156)(111,137,138,146)(112,139,127,131)(114,140,142,122)(116,136,129,125)(120,150,147,165)(121,153,148,145)(134,160,158,164)(135,161,152,157)(141,162,163,149)(144,159,155,151);(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)(102,103,108,113)(104,114,118,142)(105,110,119,133)(106,122,126,140)(107,127,124,112)(109,129,132,116)(111,136,138,125)(115,141,143,163)(117,146,128,137)(120,149,147,162)(121,152,148,135)(123,139,154,131)(130,155,156,144)(134,159,158,151)(145,164,153,160)(150,161,165,157)Polycyclic presentation:
2^7,101|a^2=g,b^2=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^100,e^b=ef,f^b=fg,h^b=h^100,d^c=dg2032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12928, 17663);