Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #12085 |
206 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 83 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) = 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)(80,82,84,85,83,86,87,81)(89,95)(94,109)(96,111)(97,107)(98,115)(102,114)(110,113)(112,118);(81,85)(82,86)(88,90,93,101)(89,94,95,109)(91,103,106,119)(92,108,104,100)(96,112,111,118)(97,113,107,110)(98,114,115,102)(99,116,117,105);(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)(80,81,84,82,83,85,87,86)(88,89)(90,98)(91,102)(92,107)(93,95)(94,99)(96,105)(97,104)(100,118)(101,115)(103,113)(106,114)(108,112)(109,117)(110,119)(111,116)Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=e,d^2=fh,e^2=g,f^2=h,b^a=bd,c^a=cgh,d^a=df,f^a=fh,i^a=i^78,c^b=cg,d^b=df,f^b=fh,i^c=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81571);