Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C157 ⋊ #1767 |
292 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 20096 |
A minimal faithful permutation representation — 3 generators on 173 points:
(1,2,5,10,19,32,49,70,95,124,117,91,116,140,135,102,73,48,67,90,115,126,97,72,51,34,21,12,6,11,20,33,50,71,96,125,148,150,143,120,142,137,106,77,52,31,46,65,86,111,130,101,76,55,38,25,15,24,37,54,75,100,129,149,155,156,153,146,139,110,81,56,35,18,29,44,61,82,107,134,105,80,59,42,28,41,58,79,104,133,123,147,154,157,151,141,114,85,60,39,22,9,16,27,40,57,78,103,132,109,84,63,45,62,83,108,136,127,94,121,145,152,144,118,89,64,43,26,13,4,7,14,23,36,53,74,99,128,113,88,66,87,112,138,131,98,69,92,119,122,93,68,47,30,17,8,3)(158,160,161,159)(167,170)(171,173);(2,4,3,6)(5,9,8,15)(7,13,12,11)(10,18,17,28)(14,22,21,24)(16,26,25,20)(19,31,30,45)(23,35,34,41)(27,39,38,37)(29,43,42,33)(32,48,47,66)(36,52,51,62)(40,56,55,58)(44,60,59,54)(46,64,63,50)(49,69,68,91)(53,73,72,87)(57,77,76,83)(61,81,80,79)(65,85,84,75)(67,89,88,71)(70,94,93,120)(74,98,97,116)(78,102,101,112)(82,106,105,108)(86,110,109,104)(90,114,113,100)(92,118,117,96)(95,123,122,146)(99,127,126,142)(103,131,130,140)(107,135,134,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,144,143,125)(145,151,150,149)(147,152,153,148)(154,157,156,155)(163,165)(166,167,168,171,169,170,172,173);(2,3)(4,6)(5,8)(7,12)(9,15)(10,17)(11,13)(14,21)(16,25)(18,28)(19,30)(20,26)(22,24)(23,34)(27,38)(29,42)(31,45)(32,47)(33,43)(35,41)(36,51)(37,39)(40,55)(44,59)(46,63)(48,66)(49,68)(50,64)(52,62)(53,72)(54,60)(56,58)(57,76)(61,80)(65,84)(67,88)(69,91)(70,93)(71,89)(73,87)(74,97)(75,85)(77,83)(78,101)(79,81)(82,105)(86,109)(90,113)(92,117)(94,120)(95,122)(96,118)(98,116)(99,126)(100,114)(102,112)(103,130)(104,110)(106,108)(107,134)(111,132)(115,128)(119,124)(121,143)(123,146)(125,144)(127,142)(129,141)(131,140)(133,139)(135,138)(136,137)(145,150)(147,153)(148,152)(149,151)(154,156)(155,157)(158,159,161,160)(162,163,164,165)Polycyclic presentation:
2^7,157|a^2=e,b^2=f,c^2=de,f^2=g,b^a=bd,h^a=h^156,c^b=cg,h^b=h^129,h^f=h^1561304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20296);