Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C79×M128 ⋊ C2 |
| Sylow | C79 ⋊ #7540 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 2 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)(80,81)(82,93)(83,99)(84,103)(85,106)(86,88)(87,107)(89,98)(90,100)(91,104)(92,109)(94,113)(95,128)(96,132)(97,110)(101,138)(102,108)(105,139)(111,142)(112,121)(114,137)(115,140)(116,126)(117,125)(118,131)(119,123)(120,122)(124,129)(127,141)(130,143)(133,136)(134,135);(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)(81,87,88,109)(82,92)(83,98)(84,100)(85,104)(89,115,113,123)(90,117,114,122)(91,118,106,112)(93,99,110,108)(94,102)(95,127)(96,131)(97,107)(101,126)(103,111,139,141)(105,137)(116,128,135,143)(119,120)(121,129)(124,138,132,136)(125,140)(130,142)(133,134)Polycyclic presentation:
2^8,79|a^2=d,c^2=efh,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^78,c^b=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh,i^b=i^783166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57456);