Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C157 ⋊ #1420 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 2 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)(158,160,165,176)(159,166,170,192)(161,178,183,207)(162,175,164,173)(163,185,187,205)(167,194,197,203)(168,198,188,190)(169,199,200,201)(171,177,204,214)(172,181,208,218)(174,179,210,186)(180,216,182,215)(184,191,195,220)(189,193,206,217)(196,209,213,221)(202,219,211,212);(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)(158,159,162,168,165,170,164,188)(160,171,173,202,176,204,175,211)(161,177,180,212,183,214,182,219)(163,184,179,200,187,195,186,169)(166,189,190,172,192,206,198,208)(167,193,196,218,197,217,213,181)(174,209,205,194,210,221,185,203)(178,199,215,220,207,201,216,191)Polycyclic presentation:
2^7,157|a^2=d,b^2=g,c^2=efg,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=ceg,d^b=dg,e^b=ef,f^b=fg,h^b=h^1561742 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 2702);