Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #13271 |
332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(80,83,85,99,87,100,86,84)(81,89,91,98,92,90,102,110)(82,94,96,111,97,95,103,101)(88,104,105,106,108,109,107,93);(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)(81,88,92,108)(83,94)(84,101)(85,96)(86,103)(87,97)(89,104,90,109)(91,105,102,107)(93,98,106,110)(95,100)(99,111);(80,81,84,90,86,91,100,110,87,92,99,89,85,102,83,98)(82,93,94,105,96,109,111,88,97,106,95,107,103,104,101,108)Polycyclic presentation:
2^8,79|a^2=f,b^2=def,c^2=e,d^2=g,e^2=h,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eh,d^b=dg,f^b=fgh,g^b=gh,i^b=i^78,i^c=i^781294 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88121);