Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1494 ⋊ C2 |
| Sylow | C79 ⋊ #8529 |
648 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 127 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)(80,82)(81,87)(83,89)(84,92)(85,90)(86,93)(88,95)(91,94)(96,99)(97,103)(98,107)(100,114)(101,112)(102,116)(104,120)(105,110)(106,122)(108,125)(109,124)(111,115)(113,123)(117,126)(118,121)(119,127);(80,81,85,88)(82,87,90,95)(83,91,84,86)(89,94,92,93)(96,98)(97,102)(99,107)(100,113)(101,109)(103,116)(104,119)(105,117)(106,121)(108,115)(110,126)(111,125)(112,124)(114,123)(118,122)(120,127);(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)(81,86)(82,89)(83,84)(88,91)(90,92)(93,94)(96,97)(98,106,109,119)(99,110,112,103)(100,104)(101,105)(102,108,117,113)(107,122)(111,120,114,118)(115,121)(116,123)(124,127)(125,126)Polycyclic presentation:
2^8,79|a^2=f,b^2=g,d^2=h,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,d^b=dh,e^b=egh,f^b=fgh,d^c=dgh,e^c=eg,f^c=fgh,i^c=i^781756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62119);