Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C79×C4⋊C32 ⋊ C2 |
| Sylow | C79 ⋊ #13641 |
180 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 151 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)(80,82,83,86)(81,85,84,87)(90,100)(95,110)(101,120)(102,121)(103,122)(111,130)(112,131)(113,132)(123,140)(124,141)(125,142)(133,145)(134,146)(135,147)(143,150)(148,151);(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)(81,84)(85,87)(88,90)(89,95)(91,101)(92,102)(93,103)(94,100)(96,111)(97,112)(98,113)(99,110)(104,123)(105,124)(106,120)(107,125)(108,121)(109,122)(114,133)(115,134)(116,130)(117,135)(118,131)(119,132)(126,143)(127,140)(128,141)(129,142)(136,148)(137,145)(138,146)(139,147)(144,150)(149,151);(80,81)(82,85)(83,84)(86,87)(88,89,91,96,92,97,104,114,93,98,105,115,107,117,126,136,94,99,106,116,108,118,127,137,109,119,128,138,129,139,144,149)(90,95,101,111,102,112,123,133,103,113,124,134,125,135,143,148,100,110,120,130,121,131,140,145,122,132,141,146,142,147,150,151)Polycyclic presentation:
2^8,79|a^2=e,c^2=d,e^2=f,f^2=g,g^2=h,b^a=bd,c^b=ch,i^b=i^78,i^c=i^783232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90101);