Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C157 ⋊ #2873 |
564 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 282 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 — 4 generators on 177 points:
(1,2,5,10,19,32,49,70,95,124,118,91,116,140,134,101,72,47,67,90,115,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,148,151,144,120,142,137,105,76,51,30,46,65,86,111,131,102,77,56,39,26,15,24,37,54,75,100,129,149,155,157,153,146,139,109,80,55,34,17,29,44,61,82,107,135,106,81,60,43,28,41,58,79,104,133,122,147,154,156,150,141,113,84,59,38,21,8,16,27,40,57,78,103,132,110,85,64,45,62,83,108,136,126,93,121,145,152,143,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,114,89,66,87,112,138,130,97,68,92,119,123,94,69,48,31,18,9,4)(163,168)(167,173)(169,175)(174,177);(2,4)(3,6)(5,9)(7,13)(8,15)(10,18)(11,12)(14,22)(16,26)(17,28)(19,31)(20,25)(21,24)(23,35)(27,39)(29,43)(30,45)(32,48)(33,42)(34,41)(36,52)(37,38)(40,56)(44,60)(46,64)(47,66)(49,69)(50,63)(51,62)(53,73)(54,59)(55,58)(57,77)(61,81)(65,85)(67,89)(68,91)(70,94)(71,88)(72,87)(74,98)(75,84)(76,83)(78,102)(79,80)(82,106)(86,110)(90,114)(92,118)(93,120)(95,123)(96,117)(97,116)(99,127)(100,113)(101,112)(103,131)(104,109)(105,108)(107,135)(111,132)(115,128)(119,124)(121,144)(122,146)(125,143)(126,142)(129,141)(130,140)(133,139)(134,138)(136,137)(145,151)(147,153)(148,152)(149,150)(154,157)(155,156)(164,170)(167,173)(171,176)(174,177);(158,159,160,161)(162,164)(163,167)(165,171)(166,170)(168,173)(169,174)(172,176)(175,177);(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)(95,122,123,146)(99,126,127,142)(103,130,131,140)(107,134,135,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,143,144,125)(145,150,151,149)(147,152,153,148)(154,156,157,155)(162,163,165,169,166,168,172,175)(164,167,171,174,170,173,176,177)Polycyclic presentation:
2^7,157|a^2=e,b^2=f,e^2=g,d^a=dg,h^a=h^129,c^b=cg,h^c=h^156,h^e=h^156848 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 21076);