Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #8641 |
336 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 111 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) = 10112 |
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)(80,82,83,89)(81,86,85,88)(84,92,91,90)(87,95,93,94)(96,98,100,107)(97,103,104,111)(99,106,102,105)(101,108,109,110);(81,85)(86,88)(87,93)(94,95)(96,97,102,109,100,104,99,101)(98,103,105,110,107,111,106,108);(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)(80,81,84,87,83,85,91,93)(82,88,90,95,89,86,92,94)(97,101)(98,105)(99,102)(104,109)(106,107)(108,110)Polycyclic presentation:
2^8,79|a^2=f,b^2=dh,c^2=h,d^2=g,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,e^c=eg,f^c=fgh,i^c=i^781756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62608);