Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1424 ⋊ C2 |
| Sylow | C79 ⋊ #13698 |
190 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 147 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)(81,83)(86,98)(91,111)(96,119)(99,110)(100,126)(101,127)(112,141)(113,137)(120,144)(121,145)(122,131)(123,139)(128,138)(129,140)(130,147)(142,146);(84,86,97,123,88,100,124,140,107,127,143,142,117,138,105,110,90,98,114,139,108,126,104,129,89,101,125,146,103,128,87,99)(85,91,102,121,93,112,132,131,109,137,135,147,136,144,116,119,95,111,134,145,118,141,115,122,94,113,133,130,106,120,92,96);(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)(82,83)(84,85,90,95)(86,96,98,119)(87,102,105,134)(88,106,108,136)(89,109,107,94)(91,110,111,99)(92,114,116,97)(93,117,118,103)(100,130,126,147)(101,131,127,122)(104,135,124,133)(112,142,141,146)(113,129,137,140)(115,125,132,143)(120,139,144,123)(121,138,145,128)Polycyclic presentation:
2^8,79|a^2=h,b^2=df,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,i^a=i^78,c^b=ch,i^c=i^781528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90422);