Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7545 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 2 generators on 147 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)(84,85,92,107,87,93,111,119,101,116,126,141,124,133,99,109,89,95,113,135,102,117,128,137,105,121,139,142,125,134,100,110,90,96,114,136,103,118,138,145,130,143,147,144,131,146,127,122,104,120,129,140,123,132,98,108,88,94,112,115,97,106,86,91);(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)(85,91)(86,92)(87,97)(88,101)(89,104)(93,115)(94,119)(95,122)(96,110)(98,126)(99,129)(100,114)(102,131)(103,125)(105,130)(106,107)(108,116)(109,120)(111,112)(113,127)(117,144)(118,142)(121,145)(123,124)(128,147)(132,141)(133,140)(134,136)(135,146)(137,143)(138,139)Polycyclic presentation:
2^8,79|a^2=d,b^2=ce,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,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, 57468);