Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #12617 |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(80,83,85,101,86,103,107,133,87,102,108,132,84,100,105,130)(81,89,91,115,92,117,121,142,93,116,122,141,90,114,119,139)(82,95,97,124,96,99,126,128,98,125,106,135,104,129,109,131)(88,110,111,136,94,113,123,137,112,127,120,143,118,138,134,140);(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)(80,82)(81,88)(83,99,102,129)(84,104)(85,106)(86,96)(87,98)(89,113,116,138)(90,118)(91,120)(92,94)(93,112)(95,103,125,100)(97,108)(101,131,132,128)(105,126)(107,109)(110,117,127,114)(111,122)(115,140,141,137)(119,123)(121,134)(124,130,135,133)(136,139,143,142);(80,81,85,91,86,92,107,121,87,93,108,122,84,90,105,119)(82,94,97,123,96,112,126,120,98,118,106,134,104,88,109,111)(83,89,101,115,103,117,133,142,102,116,132,141,100,114,130,139)(95,113,124,137,99,127,128,143,125,138,135,140,129,110,131,136)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=e,d^2=h,e^2=g,g^2=h,b^a=bd,c^b=cg,d^b=dh,e^b=eh,i^b=i^78,f^c=fh3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84688);