Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1379 ⋊ C2 |
| Sylow | C79 ⋊ #13021 |
462 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(81,90)(82,97)(84,105)(85,103)(86,112)(87,114)(88,107)(89,115)(91,120)(92,119)(93,127)(94,129)(95,122)(96,130)(98,136)(99,132)(100,137)(101,135)(102,125)(104,110)(106,109)(108,139)(111,133)(113,134)(116,138)(117,131)(118,142)(121,124)(123,143)(126,140)(128,141);(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)(80,82,87,113,88,101,109,100)(81,89,94,128,95,118,124,117)(83,97,114,134,107,135,106,137)(84,108,86,98,110,99,85,111)(90,115,129,141,122,142,121,131)(91,123,93,96,125,116,92,126)(102,138,119,140,120,143,127,130)(103,133,105,139,112,136,104,132);(80,81,86,93,87,94,110,125,88,95,85,92,109,124,84,91)(82,96,99,118,100,123,98,128,101,126,108,89,113,116,111,117)(83,102,105,129,106,127,103,90,107,120,104,121,114,119,112,122)(97,131,133,138,134,115,139,140,135,141,136,143,137,142,132,130)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfg,d^2=gh,e^2=g,f^2=g,g^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=egh,f^b=fg,g^b=gh,i^b=i^78,d^c=dgh,e^c=egh,f^c=fgh,g^c=gh,i^c=i^782230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86687);