Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #12880 |
322 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 123 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 123 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)(80,82,83,81)(85,89)(88,91)(94,102)(98,108)(103,114)(104,115)(109,118)(110,119)(116,122)(120,123);(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)(80,81,83,82)(84,86,87,90)(85,88,89,91)(92,94)(93,98)(95,103)(96,104)(97,102)(99,109)(100,110)(101,108)(105,116)(106,114)(107,115)(111,120)(112,118)(113,119)(117,122)(121,123);(81,82)(84,85)(86,88)(87,89)(90,91)(92,93,95,99,96,100,105,111,97,101,106,112,107,113,117,121)(94,98,103,109,104,110,116,120,102,108,114,118,115,119,122,123)Polycyclic presentation:
2^8,79|a^2=f,b^2=e,c^2=d,f^2=g,g^2=h,b^a=bd,c^a=ce,c^b=ch,i^b=i^78,i^c=i^783208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 85917);