Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C79×#1288 ⋊ C2 |
| Sylow | C79 ⋊ #9429 |
508 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
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)(83,85)(86,87)(88,91,93,103)(89,95,96,110)(90,98,99,113)(92,105,106,102)(94,107,109,118)(97,111,104,101)(100,117,115,114)(108,119,116,112);(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)(80,82,84,81)(83,86,85,87)(88,90,93,99)(89,94)(91,98,103,113)(92,100,106,115)(95,107)(96,109)(97,108)(101,112)(102,114,105,117)(104,116)(110,118)(111,119);(80,81,85,87,84,82,83,86)(88,89)(90,94,99,109)(91,101)(92,104)(93,96)(95,102)(97,106)(98,112,113,119)(100,116,115,108)(103,111)(105,110)(107,117,118,114)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfh,c^2=g,d^2=gh,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dh,e^b=egh,f^b=fh,i^b=i^78,d^c=dgh,e^c=eg,f^c=fgh,i^c=i^781282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 67126);