Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#359×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13071 |
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(81,89)(82,95)(84,105)(85,109)(86,101)(87,102)(88,111)(90,119)(91,117)(92,116)(93,121)(94,125)(96,131)(97,129)(98,130)(99,110)(100,107)(103,134)(104,127)(106,135)(108,128)(112,133)(113,140)(114,139)(115,120)(118,138)(122,142)(123,126)(124,137)(132,143)(136,141);(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)(80,82,94,124,85,108,84,104,87,98,106,132,86,97,107,96)(81,88,103,122,110,112,90,118,92,113,136,123,91,114,120,93)(83,95,125,137,109,128,105,127,102,130,135,143,101,129,100,131)(89,111,134,142,99,133,119,138,116,140,141,126,117,139,115,121);(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)(82,93,98,118)(83,99,102,117)(84,103)(85,91)(86,110)(87,92)(88,96,113,104)(89,101,116,109)(90,94)(95,126)(97,122,108,123)(100,115,105,119)(106,120)(107,136)(111,137)(112,132,114,124)(121,129)(125,141,135,134)(127,139)(128,138)(130,142)(131,133)(140,143)Polycyclic presentation:
2^8,79|a^2=f,b^2=dfg,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^78,d^b=dh,e^b=eh,f^b=fh,i^b=i^78,d^c=dh,e^c=eh,f^c=fh,i^c=i^781768 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 86999);