Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #7470 |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 10112 |
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)(80,81,82,83)(84,86)(85,92)(87,103)(88,106)(89,101)(90,99)(91,102)(93,116)(94,119)(95,114)(96,98)(97,115)(100,109)(104,127)(105,131)(107,134)(108,112)(110,128)(111,130)(113,122)(117,125)(118,140)(120,142)(121,133)(123,126)(124,139)(129,136)(132,146)(135,137)(138,144)(141,145)(143,147);(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)(84,85,88,94,89,95,107,120,90,96,108,121,110,123,135,143,91,97,109,122,111,124,136,144,87,93,104,117,105,118,132,141)(86,98,100,125,101,126,129,145,99,115,127,119,128,139,146,142,102,116,106,133,130,140,134,147,103,92,112,113,131,114,137,138)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,i^a=i^78,c^b=ch,d^b=dh3232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57266);