Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1978 ⋊ C2 |
| Sylow | C79 ⋊ #13036 |
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 105 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)(81,88)(82,94)(84,99)(85,102)(86,105)(87,101)(89,110)(90,107)(91,106)(92,109)(93,111)(95,97)(96,108)(98,104)(100,103);(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)(80,82,86,81,87,96,103,92)(83,94,105,88,101,108,100,109)(84,90,85,95,93,89,104,91)(97,111,110,98,106,99,107,102);(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)(80,81,85,91,103,96,84,90,87,92,104,95,86,82,93,89)(83,97,99,88,105,107,102,94,101,106,111,109,100,110,98,108)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfgh,d^2=g,e^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^78,d^b=dg,e^b=egh,f^b=fg,g^b=gh,i^b=i^78,d^c=dgh,e^c=egh,f^c=fgh,g^c=gh,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, 86796);