Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#1516 ⋊ C2 |
| Sylow | C79 ⋊ #8463 |
718 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)(80,83,84,91)(81,86,87,93)(82,89,90,95)(85,92,88,94)(96,99)(97,104)(98,109)(100,115)(101,113)(102,114)(103,116)(105,121)(106,119)(107,120)(108,122)(110,126)(111,125)(112,124)(117,127)(118,123);(80,82)(81,85)(83,89)(84,90)(86,92)(87,88)(91,95)(93,94)(96,98)(97,103)(99,109)(100,112)(101,110)(102,111)(104,116)(105,118)(106,108)(107,117)(113,126)(114,125)(115,124)(119,122)(120,127)(121,123);(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)(82,88,90,85)(83,86)(84,87)(89,94,95,92)(91,93)(96,97,101,106,102,107,100,105)(98,108,112,103,111,118,110,117)(99,104,113,119,114,120,115,121)(109,123,124,127,125,122,126,116)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,i^a=i^78,d^b=dh,e^b=eh,f^b=fgh,d^c=dh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 61748);