Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7542 |
86 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)(80,82,87,100)(81,88,94,124)(83,102,107,148)(84,108,111,97)(85,113,115,146)(86,117,118,176)(89,126,131,142)(90,123,93,120)(91,135,137,140)(92,138,139,185)(95,101,145,161)(96,105,150,171)(98,103,153,114)(99,155,156,110)(104,167,169,162)(106,173,174,207)(109,178,179,182)(112,121,127,187)(116,122,133,188)(119,125,147,190)(128,194,130,191)(129,197,198,203)(132,199,136,200)(134,175,166,151)(141,160,144,157)(143,172,201,205)(149,189,202,206)(152,158,193,196)(154,159,192,195)(163,165,183,170)(164,204,181,168)(177,186,180,184);(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)(80,81,84,90,87,94,111,93)(82,95,97,141,100,145,108,144)(83,101,104,157,107,161,169,160)(85,112,109,177,115,127,179,180)(86,116,110,92,118,133,155,139)(88,119,120,96,124,147,123,150)(89,125,128,171,131,190,130,105)(91,134,132,103,137,166,136,114)(98,152,151,197,153,193,175,203)(99,154,117,143,156,192,176,201)(102,135,162,200,148,140,167,199)(106,172,168,159,174,205,204,195)(113,142,182,194,146,126,178,191)(121,173,184,181,187,207,186,164)(122,149,185,183,188,202,138,163)(129,165,196,206,198,170,158,189)Polycyclic presentation:
2^8,79|a^2=d,b^2=h,c^2=efh,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=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh1528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57461);