Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#1468 ⋊ C2 |
| Sylow | C79 ⋊ #8488 |
768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 119 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,83,84,87)(81,85,86,82)(88,91)(89,96)(90,101)(92,107)(93,105)(94,106)(95,108)(97,113)(98,111)(99,112)(100,114)(102,118)(103,117)(104,116)(109,119)(110,115);(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)(81,83)(84,85)(86,87)(88,90)(89,95)(91,101)(92,104)(93,102)(94,103)(96,108)(97,110)(98,100)(99,109)(105,118)(106,117)(107,116)(111,114)(112,119)(113,115);(80,81)(82,87,85,83)(84,86)(88,89,93,98,94,99,92,97)(90,100,104,95,103,110,102,109)(91,96,105,111,106,112,107,113)(101,115,116,119,117,114,118,108)Polycyclic presentation:
2^8,79|a^2=f,c^2=g,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=egh,f^b=fgh,i^b=i^78,d^c=dgh,f^c=fg1285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 61900);