Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C79 ⋊ #13721 |
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 151 points:
(1,2)(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)(81,85)(84,87)(88,91,92,110,115,142,137,108,95,112,116,141,122,106,93,109,96,113,117,143,148,138,119,140,121,144,136,107,94,111,105,90)(89,98,99,128,120,150,147,145,102,129,130,125,132,134,100,97,103,104,118,133,149,139,131,126,123,135,146,151,101,124,114,127);(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)(80,82,83,86)(81,84,85,87)(88,90,105,111,94,107,136,144,121,140,119,138,148,143,117,113,96,109,93,106,122,141,116,112,95,108,137,142,115,110,92,91)(89,97,114,134,101,125,146,129,123,145,131,150,149,128,118,98,103,127,100,124,132,151,130,135,102,126,147,139,120,133,99,104);(80,81)(82,84)(83,85)(86,87)(88,89)(90,104)(91,97)(92,114)(93,118)(94,120)(95,123)(96,103)(98,109)(99,105)(100,117)(101,115)(102,121)(106,128)(107,139)(108,129)(110,134)(111,133)(112,145)(113,127)(116,131)(119,130)(122,149)(124,143)(125,142)(126,144)(132,148)(135,140)(136,147)(137,146)(138,151)(141,150)Polycyclic presentation:
2^8,79|b^2=eh,c^2=d,d^2=fg,e^2=f,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=efg,f^a=fg,g^a=gh,i^b=i^78,i^c=i^781552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90544);