Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#2239 ⋊ C2 |
| Sylow | C79 ⋊ #12303 |
322 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 points:
(1,3,7,17)(2,9,13,25)(4,15,21,31)(5,22,6,16)(8,23,18,32)(10,26,27,24)(11,28,12,14)(19,29,20,30)(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)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110);(2,8)(4,19)(5,6)(9,23)(10,11)(12,27)(13,18)(14,24)(15,29)(16,22)(20,21)(25,32)(26,28)(30,31)(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)(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);(1,2,6,11,7,13,5,12)(3,14,16,9,17,28,22,25)(4,18,20,10,21,8,19,27)(15,26,30,23,31,24,29,32)Polycyclic presentation:
2^8,79|a^2=fg,c^2=h,d^2=f,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,g^a=gh,d^b=dfh,e^b=egh,f^b=fh,i^b=i^78,d^c=dg,e^c=eh,i^c=i^78,e^d=eh805 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 82920);