Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7538 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 20224 |
A minimal faithful permutation representation — 2 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)(84,85,90,95)(86,97,101,126)(87,102,105,137)(88,106,108,140)(89,109,107,94)(91,110,113,96)(92,115,117,98)(93,119,120,103)(99,130,132,146)(100,134,131,125)(104,139,127,136)(111,143,144,129)(112,124,121,133)(114,141,145,122)(116,128,135,138)(118,142,147,123);(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)(80,81,82,83)(85,91)(86,96)(87,98)(88,103)(89,107)(92,114)(93,118)(94,121)(95,113)(97,102)(99,129)(100,133)(101,110)(104,138)(105,115)(106,111)(108,119)(109,112)(116,146)(117,145)(120,147)(122,123)(124,131)(125,139)(126,137)(127,128)(130,135)(132,143)(134,136)(140,144)(141,142)Polycyclic presentation:
2^8,79|a^2=d,b^2=h,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^78,c^b=ce,e^b=ef,f^b=fg,g^b=gh,i^b=i^785062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57450);