Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7539 |
88 conjugacy classes of subgroups.
| minimal degree | μ(G) = 207 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 2 generators on 207 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,82)(81,89)(83,102)(84,97)(85,112)(86,117)(87,120)(88,100)(90,128)(91,122)(92,134)(93,136)(94,126)(95,101)(96,105)(98,103)(99,113)(104,153)(106,165)(107,168)(108,156)(109,170)(110,148)(111,123)(114,176)(115,174)(116,124)(118,178)(119,125)(121,127)(129,188)(130,191)(131,190)(132,193)(133,144)(135,195)(137,182)(138,149)(139,164)(140,167)(141,152)(142,198)(143,163)(145,150)(146,159)(147,151)(154,157)(155,161)(158,173)(160,204)(162,180)(166,207)(169,181)(171,194)(172,184)(175,183)(177,186)(179,189)(185,187)(192,199)(196,202)(197,206)(200,201)(203,205);(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)(80,81,84,91,88,94,87,119)(82,95,97,138,100,141,120,140)(83,101,104,149,108,152,107,167)(85,111,109,169,115,172,114,175)(86,116,110,137,118,177,113,93)(89,121,122,143,126,180,125,96)(90,127,129,163,131,162,179,105)(92,133,132,159,135,158,171,103)(98,145,144,199,146,200,173,191)(99,147,117,139,148,196,178,197)(102,134,153,193,156,195,168,194)(106,164,160,202,166,206,161,151)(112,128,170,188,174,190,176,189)(123,165,181,204,184,207,183,155)(124,185,182,203,186,142,136,154)(130,157,150,187,192,205,201,198)Polycyclic presentation:
2^8,79|a^2=d,c^2=ef,d^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^78,c^b=ce,e^b=ef,f^b=fg,g^b=gh1552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57452);