Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #510×C157 ⋊ C2 |
| Sylow | C157 ⋊ #2195 |
206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 3 generators on 221 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,161,165,180)(159,167,171,193)(160,173,176,205)(162,178,185,212)(163,186,164,179)(166,189,191,217)(168,192,196,209)(169,197,170,177)(172,199,200,220)(174,202,188,215)(175,204,187,203)(181,208,195,219)(182,210,213,221)(183,214,184,211)(190,216,198,207)(194,218,206,201);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150,152,154,156,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(158,160)(159,166)(161,173)(162,182)(163,175)(164,187)(165,176)(167,189)(168,194)(169,190)(170,198)(171,191)(172,181)(174,184)(177,207)(178,210)(179,203)(180,205)(183,188)(185,213)(186,204)(192,218)(193,217)(195,200)(196,206)(197,216)(199,208)(201,209)(202,211)(212,221)(214,215)(219,220);(158,159,165,171)(160,172,176,200)(161,177,180,197)(162,181,185,195)(163,170,164,169)(166,188,191,174)(167,186,193,179)(168,183,196,184)(173,201,205,218)(175,206,187,194)(178,209,212,192)(182,198,213,190)(189,210,217,221)(199,204,220,203)(202,207,215,216)(208,214,219,211)Polycyclic presentation:
2^7,157|a^2=g,c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,e^c=eg,h^c=h^1561271 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 6485);