Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1344 ⋊ C2 |
| Sylow | C79 ⋊ #12095 |
458 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 119 points:
(9,12,14,25)(10,16,18,32)(11,20,22,23)(13,26,27,24)(15,28,29,30)(17,31,33,40)(19,34,35,39)(21,37,38,36)(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)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118);(2,5)(3,8)(6,7)(9,11,14,22)(10,15,18,29)(12,23,25,20)(13,21,27,38)(16,30,32,28)(17,19,33,35)(24,37,26,36)(31,39,40,34);(1,2)(3,5)(4,7)(6,8)(9,10)(11,19)(12,16)(13,17)(14,18)(15,21)(20,34)(22,35)(23,39)(24,31)(25,32)(26,40)(27,33)(28,36)(29,38)(30,37)(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)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)Polycyclic presentation:
2^8,79|b^2=h,c^2=h,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=gh,i^a=i^78,c^b=ch,d^b=df,e^b=egh,d^c=dg,i^c=i^78,e^d=eh922 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81627);