Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C8 |
No aliases for this group.
| Sylow | C79 ⋊ #12514 |
246 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 3 generators on 127 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)(81,86)(85,93)(87,91)(88,94)(96,99,119,116,103,114,101,117,104,113,100,115,102,120,121,98)(97,106,125,124,110,122,108,118,111,112,107,123,109,126,127,105);(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)(80,82,83,89,84,90,92,95)(81,85,87,88,86,93,91,94)(96,98,101,114,102,115,119,99,104,117,121,120,103,116,100,113)(97,105,108,122,109,123,125,106,111,118,127,126,110,124,107,112);(80,81)(82,88)(83,91)(84,86)(85,89)(87,92)(90,94)(93,95)(96,97,104,111)(98,112,117,106)(99,118,113,105)(100,108,119,127)(101,107,121,125)(102,110,103,109)(114,124,120,123)(115,126,116,122)Polycyclic presentation:
2^8,79|a^2=h,b^2=dgh,c^2=ef,d^2=fh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,c^b=ch,i^b=i^78,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, 84275);