Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1379 ⋊ C2 |
| Sylow | C79 ⋊ #13489 |
278 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(80,83)(81,89,90,115)(82,95)(84,101)(85,106)(86,110)(87,103)(88,111,94,124)(91,99,93,123)(92,120,117,143)(96,127)(97,130)(98,129)(100,105)(102,107)(104,136)(108,140)(109,128)(112,141,122,126)(113,133,125,132)(114,137,142,119)(116,118,139,121)(131,134)(135,138);(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)(81,88)(83,100)(84,96)(85,105)(86,109)(87,98)(89,114)(90,94)(91,112)(92,119)(93,122)(95,102)(97,107)(99,132)(101,134)(103,135)(104,131)(106,127)(108,138)(110,130)(111,116)(113,121)(115,142)(117,137)(118,125)(120,141)(123,133)(124,139)(126,143)(128,140)(129,136);(80,81)(82,94,98,88)(83,99,103,123)(84,91)(85,92)(86,93)(87,90)(89,101,115,110)(95,126)(96,122,109,112)(97,125,131,113)(100,133)(102,120,136,143)(104,118)(105,137,138,119)(106,139,140,116)(107,121)(108,117)(111,127)(114,134)(124,128)(129,141)(130,142)(132,135)Polycyclic presentation:
2^8,79|a^2=eg,c^2=d,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,c^b=cf,f^b=fg,g^b=gh,i^b=i^78,f^c=fg,g^c=gh,i^c=i^782224 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89405);