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 ⋊ #13016 |
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)(82,96)(84,107)(85,112)(86,103)(87,114)(88,106)(89,115)(91,102)(92,119)(93,127)(94,122)(95,128)(97,132)(98,131)(99,135)(100,136)(101,134)(104,109)(105,108)(110,138)(111,139)(113,133)(116,143)(117,130)(118,142)(120,125)(121,124)(123,137)(126,141)(129,140);(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)(80,82,87,113,88,101,108,100)(81,89,93,126,94,118,124,117)(83,96,114,133,106,134,105,136)(84,98,86,97,109,99,85,111)(90,115,127,141,122,142,121,130)(91,123,92,95,125,116,110,129)(102,137,119,128,120,143,138,140)(103,132,104,135,112,139,107,131);(80,81,86,92,87,93,109,125,88,94,85,110,108,124,84,91)(82,95,99,118,100,123,97,126,101,129,98,89,113,116,111,117)(83,102,104,127,105,138,103,90,106,120,107,121,114,119,112,122)(96,130,132,137,133,115,135,128,134,141,139,143,136,142,131,140)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,e^a=eh,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^78,d^c=dg,e^c=egh,f^c=fg,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, 86652);