Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | #102×C157 ⋊ C4 |
| Sylow | C157 ⋊ #1764 |
300 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 177 |
| transitive degree | μt(G) = 5024 |
A minimal faithful permutation representation — 3 generators on 177 points:
(1,2,7,3)(4,6,17,13)(5,8,15,9)(10,12,31,27)(11,18,25,19)(14,16,29,23)(20,22,49,41)(21,32,39,33)(24,30,45,37)(26,28,47,43)(34,36,71,59)(35,50,57,51)(38,48,63,55)(40,42,69,65)(44,46,67,61)(52,54,97,81)(53,72,79,73)(56,70,85,77)(58,60,95,87)(62,68,91,83)(64,66,93,89)(74,76,127,107)(75,98,105,99)(78,96,111,103)(80,82,125,113)(84,94,117,109)(86,88,123,119)(90,92,121,115)(100,102,149,137)(101,128,135,129)(104,126,141,133)(106,108,148,142)(110,124,145,139)(112,114,131,146)(116,122,140,144)(118,120,134,147)(130,132,143,151)(136,138,155,153)(150,152,154,157)(162,164,166,173,167,174,165,172)(163,169,170,176,171,177,168,175);(2,4,5,3)(6,10,11,9)(7,8,14,13)(12,20,21,19)(15,18,24,23)(16,26,27,17)(22,34,35,33)(25,32,38,37)(28,40,41,31)(29,30,44,43)(36,52,53,51)(39,50,56,55)(42,58,59,49)(45,48,62,61)(46,64,65,47)(54,74,75,73)(57,72,78,77)(60,80,81,71)(63,70,84,83)(66,86,87,69)(67,68,90,89)(76,100,101,99)(79,98,104,103)(82,106,107,97)(85,96,110,109)(88,112,113,95)(91,94,116,115)(92,118,119,93)(102,130,131,129)(105,128,134,133)(108,136,137,127)(111,126,140,139)(114,132,142,125)(117,124,145,144)(120,135,146,123)(121,122,141,147)(138,150,151,149)(143,152,153,148)(154,156,157,155)(158,159,160,161)(163,168,171,170)(169,175,177,176);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,56,50)(42,49,59,58)(45,61,62,48)(46,47,65,64)(54,73,75,74)(57,77,78,72)(60,71,81,80)(63,83,84,70)(66,69,87,86)(67,89,90,68)(76,99,101,100)(79,103,104,98)(82,97,107,106)(85,109,110,96)(88,95,113,112)(91,115,116,94)(92,93,119,118)(102,129,131,130)(105,133,134,128)(108,127,137,136)(111,139,140,126)(114,125,142,132)(117,144,145,124)(120,123,146,135)(121,147,141,122)(138,149,151,150)(143,148,153,152)(154,155,157,156)(162,163,166,170,167,171,165,168)(164,169,173,176,174,177,172,175)Polycyclic presentation:
2^7,157|a^2=e,b^2=f,c^2=e,d^2=g,e^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^129,h^b=h^28,h^c=h^129,h^e=h^156,h^f=h^156602 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20285);