Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #10668 |
316 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 97 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)(80,82,85,81)(83,87,84,86)(88,91)(89,95)(90,98)(92,104)(93,102)(94,106)(96,111)(97,110)(99,116)(100,114)(101,112)(103,105)(107,118)(108,109)(113,119)(115,117);(81,86)(82,87)(83,84)(88,90,92,99,93,100,105,117)(89,94,96,107,97,108,112,119)(91,98,104,116,102,114,103,115)(95,109,111,113,110,106,101,118);(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)(80,81,83,87,85,82,84,86)(88,89)(90,94)(91,101,102,111)(92,96)(93,97)(95,103,110,104)(98,113,114,118)(99,107)(100,108)(105,112)(106,115,109,116)(117,119)Polycyclic presentation:
2^8,79|a^2=d,b^2=de,c^2=g,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,f^a=fgh,i^a=i^78,c^b=cf,d^b=dg,e^b=eg,f^b=fg,d^c=dh,e^c=eh,f^c=fg,i^c=i^781756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 74590);