Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | #125×C157 ⋊ C4 |
| Sylow | C157 ⋊ #1412 |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 2512 |
A minimal faithful permutation representation — 2 generators on 173 points:
(1,2,5,10,19,32,49,70,95,124,97,68,92,119,142,114,89,66,87,112,140,147,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,150,126,93,121,138,110,85,64,45,62,83,108,136,145,113,84,59,38,21,8,16,27,40,57,78,103,131,152,155,148,122,134,106,81,60,43,28,41,58,79,104,132,141,109,80,55,34,17,29,44,61,82,107,135,153,157,156,151,130,102,77,56,39,26,15,24,37,54,75,100,129,137,105,76,51,30,46,65,86,111,139,120,146,154,149,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,133,101,72,47,67,90,115,143,118,91,116,144,123,94,69,48,31,18,9,4)(158,160,162,168)(159,163)(161,170,171,169)(164,167)(165,172)(166,173);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,135)(99,126,127,146)(103,124,130,144)(107,133,134,140)(111,137,138,136)(115,141,142,132)(119,145,143,129)(121,147,139,125)(128,148,149,153)(131,150,151,154)(152,155,156,157)(158,159)(160,167,169,173)(161,165,171,164)(162,166)(163,168,172,170)Polycyclic presentation:
2^7,157|a^2=d,b^2=f,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^28,c^b=cf,d^b=def,e^b=eg,d^c=dfg,e^d=eg,h^d=h^156560 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 19650);