Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1383 ⋊ C2 |
| Sylow | C79 ⋊ #13009 |
496 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(85,92)(87,102)(88,103)(91,108)(95,107)(97,104)(99,115)(110,113);(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)(80,82,83,81)(84,86,89,106,90,98,105,100)(85,91,107,110,92,108,95,113)(87,99,103,97,102,115,88,104)(93,112,111,114,101,109,94,96);(80,81,83,82)(84,85,88,94,105,107,102,93,90,92,103,111,89,95,87,101)(86,96,99,91,106,109,97,113,98,114,115,108,100,112,104,110)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfg,d^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^78,d^c=dh,f^c=fh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86607);