Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #13732 |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 151 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(88,90,101,127,93,104,128,145,108,131,147,146,122,143,106,117,91,102,120,144,107,130,111,133,94,105,129,150,110,132,92,103)(89,96,109,125,98,118,138,135,113,141,140,151,137,148,115,123,95,114,136,149,116,142,121,126,99,119,139,134,112,124,97,100);(80,82,83,87)(81,84,85,86)(89,95)(96,114)(97,115)(98,116)(99,113)(100,123)(109,136)(112,137)(118,142)(119,141)(121,138)(124,148)(125,149)(126,135)(134,151)(139,140);(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)(80,81,83,85)(82,86,87,84)(88,89,91,95)(90,100,102,123)(92,109,106,136)(93,112,107,137)(94,113,108,99)(96,117,114,103)(97,120,115,101)(98,122,116,110)(104,134,130,151)(105,135,131,126)(111,140,128,139)(118,146,142,150)(119,133,141,145)(121,129,138,147)(124,144,148,127)(125,143,149,132)Polycyclic presentation:
2^8,79|a^2=d,b^2=dh,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^785062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90592);