Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1381 ⋊ C2 |
| Sylow | C79 ⋊ #12995 |
476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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)(84,109)(85,112)(86,113)(87,105)(88,107)(89,114)(91,123)(92,126)(93,127)(94,103)(95,121)(96,128)(98,135)(99,137)(100,138)(101,132)(102,134)(104,111)(106,110)(108,133)(115,139)(116,143)(117,141)(118,142)(119,125)(120,124)(122,130)(129,140)(131,136);(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)(80,82,87,99,88,102,85,101)(81,89,94,115,95,118,92,117)(83,97,105,137,107,134,112,132)(84,108,86,98,111,100,110,136)(90,114,103,139,121,142,126,141)(91,122,93,96,125,116,124,129)(104,138,106,131,109,133,113,135)(119,143,120,140,123,130,127,128);(80,81,86,93,87,94,111,125,88,95,110,124,85,92,84,91)(82,96,100,118,101,122,98,115,102,129,108,89,99,116,136,117)(83,103,106,123,105,121,109,127,107,126,113,119,112,90,104,120)(97,130,133,141,132,140,131,142,134,143,138,139,137,128,135,114)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfg,d^2=gh,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^78,d^c=dh,e^c=eh,f^c=fh,i^c=i^781762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86525);