Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7547 |
60 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)(80,82,96,136,85,99,137,187,112,148,191,207,158,193,107,143,87,101,139,189,113,149,162,195,116,152,192,206,159,194,108,144,88,102,140,190,114,150,160,174,110,146,179,176,128,172,105,118,84,98,123,173,109,145,106,142,86,100,138,188,104,141,83,97)(81,89,103,133,92,120,155,151,115,168,161,196,164,181,124,132,91,119,154,184,127,175,180,186,130,178,203,198,166,183,126,135,94,122,157,185,129,177,202,200,169,205,204,199,167,201,171,153,117,170,163,197,165,182,125,134,93,121,156,147,111,131,90,95);(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)(80,81,84,91,88,94,87,117)(82,95,98,132,102,135,101,153)(83,103,105,154,108,157,107,163)(85,111,109,164,114,166,113,167)(86,115,110,130,116,169,112,93)(89,118,119,144,122,143,170,97)(90,123,124,140,126,139,171,96)(92,128,127,159,129,158,165,104)(99,147,145,196,150,198,149,199)(100,151,146,186,152,200,148,134)(106,161,160,203,162,204,137,156)(120,176,175,206,177,207,182,188)(121,142,168,174,178,195,205,187)(125,138,155,179,180,192,202,191)(131,173,181,190,183,189,201,136)(133,172,184,194,185,193,197,141)Polycyclic presentation:
2^8,79|a^2=d,b^2=ce,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^785062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57472);