Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1974 ⋊ C2 |
| Sylow | C79 ⋊ #13011 |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 115 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)(84,87)(85,94)(86,89)(88,104)(90,106)(91,102)(92,101)(93,95)(96,112)(97,105)(98,115)(99,110)(100,107)(103,108)(109,111)(113,114);(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)(81,83)(84,86,100,103,92,104,91,106)(85,93,109,105,99,112,98,113)(87,89,107,108,101,88,102,90)(94,95,111,97,110,96,115,114);(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)(84,85,90,97,91,98,88,95,92,99,108,114,100,109,89,96)(86,94,102,93,103,111,87,105,104,110,107,112,106,115,101,113)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfg,d^2=gh,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,i^a=i^78,d^b=dg,e^b=eg,f^b=fg,g^b=gh,i^b=i^78,d^c=dg,e^c=eg,f^c=fg,g^c=gh,i^c=i^781774 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86621);