Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1395 ⋊ C2 |
| Sylow | C79 ⋊ #13097 |
650 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 89 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:
(1,2)(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)(80,83,85,92)(81,87,90,105)(82,93,96,94)(84,100,101,98)(86,102,104,108)(88,106,97,89)(91,103,109,107)(95,111,99,110);(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)(80,82,92,94,85,96,83,93)(81,86,97,109,90,104,88,91)(84,99,100,110,101,95,98,111)(87,102,89,107,105,108,106,103);(80,81)(82,91,96,109)(83,97,92,88)(84,89)(85,90)(86,94)(87,98,105,100)(93,104)(95,108,99,102)(101,106)(103,111)(107,110)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^78,d^c=dh,e^c=eh,f^c=fh,i^c=i^78,f^d=fh1048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 87133);