Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C157 ⋊ #1581 |
182 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 10048 |
A minimal faithful permutation representation — 3 generators on 173 points:
(1,2,7,3)(4,11,14,8)(5,16,12,6)(9,24,23,17)(10,29,25,15)(13,20,27,21)(18,41,36,30)(19,46,42,28)(22,37,40,34)(26,33,44,38)(31,62,53,47)(32,67,63,45)(35,58,57,51)(39,54,61,55)(43,50,65,59)(48,87,74,68)(49,92,88,66)(52,83,78,72)(56,79,82,76)(60,75,86,80)(64,71,90,84)(69,116,99,93)(70,121,117,91)(73,112,103,97)(77,108,107,101)(81,104,111,105)(85,100,115,109)(89,96,119,113)(94,142,128,122)(95,147,143,120)(98,140,132,126)(102,138,135,130)(106,136,131,134)(110,133,127,137)(114,129,123,139)(118,125,145,141)(124,149,152,146)(144,148,154,150)(151,155,156,153)(158,160,161,163,162,164,165,159);(167,170)(168,173)(171,172);(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)(158,159,161,160,162,163,165,164)(166,167)(168,170)(169,172)(171,173)Polycyclic presentation:
2^7,157|a^2=e,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^129,d^b=df,h^c=h^129,h^e=h^156584 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20109);