Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #8478 |
656 conjugacy classes of subgroups.
| minimal degree | μ(G) = 127 |
| transitive degree | μt(G) = 10112 |
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)(80,83,85,82)(81,87,88,86)(84,90,92,91)(89,93,95,94)(96,99,101,112)(97,103,105,110)(98,107,109,124)(100,115,116,111)(102,117,118,126)(104,121,113,119)(106,122,120,127)(108,125,114,123);(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)(80,82,85,83)(81,86,88,87)(84,91,92,90)(89,94,95,93)(96,98,101,109)(97,102,105,118)(99,107,112,124)(100,114,116,108)(103,117,110,126)(104,120,113,106)(111,125,115,123)(119,122,121,127);(80,81,84,89,85,88,92,95)(82,87,90,94,83,86,91,93)(96,97)(98,106)(99,110,112,103)(100,113)(101,105)(102,108)(104,116)(107,122,124,127)(109,120)(111,119,115,121)(114,118)(117,123,126,125)Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=g,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dh,e^b=eh,f^b=fgh,i^b=i^78,d^c=dh,f^c=fg,i^c=i^781522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 61833);