Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C79×#2148 ⋊ C2 |
| Sylow | C79 ⋊ #12746 |
886 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(81,89)(82,94)(84,104)(85,108)(86,100)(87,101)(88,111)(90,119)(91,98)(92,117)(93,121)(95,128)(96,125)(97,127)(99,107)(102,131)(103,135)(105,133)(106,138)(109,116)(110,126)(112,141)(113,140)(114,130)(115,120)(118,143)(122,142)(123,139)(124,129)(132,136)(134,137);(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)(81,88)(83,94)(84,103)(85,97)(86,110)(87,96)(89,111)(90,118)(91,114)(92,112)(93,102)(95,106)(98,130)(99,132)(100,126)(101,125)(104,135)(105,129)(107,136)(108,127)(109,113)(115,142)(116,140)(117,141)(119,143)(120,122)(121,131)(123,134)(124,133)(128,138)(137,139);(80,81,85,92,87,91,86,109)(82,93,97,122,96,123,110,118)(83,98,100,117,101,89,108,116)(84,102,105,120,107,134,106,90)(88,103,112,129,114,136,113,95)(94,121,126,143,125,139,127,142)(99,131,133,119,104,137,138,115)(111,132,140,124,130,135,141,128)Polycyclic presentation:
2^8,79|a^2=f,d^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,d^b=dg,e^b=eh,g^b=gh,i^b=i^78,d^c=dh,f^c=fh,i^c=i^781294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85279);