Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #8677 |
366 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 119 points:
(1,2)(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)(80,81,83,85)(82,87,86,84)(88,91,93,105)(89,95,97,103)(90,100,102,116)(92,104,99,113)(94,107,108,117)(96,109,106,118)(98,110,111,114)(101,115,112,119);(88,90,99,112,93,102,92,101)(89,94,106,111,97,108,96,98)(91,100,113,119,105,116,104,115)(95,107,118,114,103,117,109,110);(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)(81,84)(82,86)(85,87)(88,89)(90,98)(91,103,105,95)(92,106)(93,97)(94,101)(96,99)(100,114,116,110)(102,111)(104,109,113,118)(107,115,117,119)(108,112)Polycyclic presentation:
2^8,79|a^2=f,b^2=dg,c^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,e^c=egh,f^c=fg,i^c=i^782230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62788);