Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C79×#1306 ⋊ C2 |
| Sylow | C79 ⋊ #9512 |
558 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 558 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)(80,83,84,90)(81,86,87,93)(82,88,89,94)(85,91,92,95)(96,99,101,107)(97,102,103,106)(98,105,104,111)(100,109,110,108);(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)(81,85,87,92)(83,88)(84,89)(86,91,93,95)(90,94)(96,98,100,103,101,104,110,97)(99,105,109,106,107,111,108,102);(80,81)(82,85,89,92)(83,86)(84,87)(88,91,94,95)(90,93)(96,97,100,104,101,103,110,98)(99,106,108,111,107,102,109,105)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,d^b=dg,e^b=eh,f^b=fg,i^b=i^78,d^c=dh,f^c=fh,i^c=i^781051 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 67551);