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 ⋊ #8675 |
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:
(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)(82,87,86,84)(88,91,93,104)(89,95,97,102)(90,99,101,114)(92,103,106,118)(94,107,108,116)(96,109,105,117)(98,110,111,112)(100,113,115,119);(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)(88,90,92,100,93,101,106,115)(89,94,96,98,97,108,105,111)(91,99,103,113,104,114,118,119)(95,107,109,110,102,116,117,112);(81,84)(82,86)(85,87)(88,89)(90,98)(91,102,104,95)(92,105)(93,97)(94,100)(96,106)(99,112,114,110)(101,111)(103,109,118,117)(107,113,116,119)(108,115)Polycyclic presentation:
2^8,79|a^2=f,b^2=d,c^2=h,d^2=g,e^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,e^c=egh,f^c=fg,i^c=i^781762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62774);