Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #13015 |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 119 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)(88,90,94,105)(89,96,100,115)(91,107,92,110)(93,111,108,104)(95,112,113,101)(97,116,98,118)(99,119,117,114)(102,109,103,106);(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)(80,82,83,81)(85,87)(89,95)(91,106)(92,109)(93,108)(96,112)(97,99)(98,117)(100,113)(101,115)(102,107)(103,110)(104,111)(114,118)(116,119);(80,81,83,82)(84,85,86,87)(88,89,92,98,108,117,106,95,94,100,91,97,93,99,109,113)(90,101,103,119,111,116,107,115,105,112,102,114,104,118,110,96)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfgh,c^2=h,d^2=gh,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^78,d^c=dg,e^c=eg,f^c=fg,g^c=gh,i^c=i^783178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86645);