Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1342 ⋊ C2 |
| Sylow | C79 ⋊ #12118 |
392 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 53 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:
(1,4)(2,10)(3,16)(5,26)(6,29)(7,22)(8,23)(9,32)(11,36)(12,40)(13,20)(14,37)(15,42)(17,49)(18,47)(19,48)(21,28)(24,54)(25,59)(27,57)(30,58)(31,46)(33,53)(34,60)(35,61)(38,62)(39,55)(41,63)(43,64)(44,52)(45,51)(50,56)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142);(1,3,8,19)(2,9,14,35)(4,16,23,48)(5,25,28,50)(6,18,7,31)(10,32,37,61)(11,38,39,52)(12,34,13,33)(15,41,43,24)(17,30,51,27)(20,53,40,60)(21,56,26,59)(22,46,29,47)(36,62,55,44)(42,63,64,54)(45,57,49,58);(1,2)(3,15)(4,20)(5,24)(6,13)(7,12)(8,14)(9,17)(10,22)(11,27)(16,44)(18,52)(19,43)(21,55)(23,40)(25,33)(26,36)(28,41)(29,37)(30,39)(31,38)(32,59)(34,50)(35,51)(42,46)(45,53)(47,64)(48,62)(49,60)(54,58)(56,61)(57,63)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)Polycyclic presentation:
2^8,79|b^2=h,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,g^a=gh,i^a=i^78,d^b=df,e^b=egh,f^b=fh,d^c=dg,e^c=eh,i^c=i^78,e^d=eh805 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81756);