Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Sylow | C79 ⋊ #12542 |
350 conjugacy classes of subgroups.
| 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)(81,88)(82,92,94,115)(84,97)(85,99)(86,98)(87,103,105,126)(89,108)(90,110)(91,109)(93,114,116,136)(95,96,118,120)(100,122)(101,121)(102,123)(104,125,127,140)(106,107,129,131)(111,133)(112,132)(113,134)(117,119,137,138)(124,139)(128,130,141,142)(135,143);(80,82)(81,87)(83,96,98,120)(84,93)(85,95)(86,94)(88,107,109,131)(89,104)(90,106)(91,105)(92,99,115,123)(97,119,121,138)(100,117)(101,116)(102,118)(103,110,126,134)(108,130,132,142)(111,128)(112,127)(113,129)(114,122,136,139)(124,137)(125,133,140,143)(135,141);(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)(80,81,84,89,85,90,100,111,86,91,101,112,102,113,124,135)(82,87,93,104,95,106,117,128,94,105,116,127,118,129,137,141)(83,88,97,108,99,110,122,133,98,109,121,132,123,134,139,143)(92,103,114,125,96,107,119,130,115,126,136,140,120,131,138,142)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,c^2=f,d^2=g,g^2=h,i^a=i^78,c^b=cg,f^b=fh,e^c=eh,i^c=i^781804 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 84402);