Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1423 ⋊ C2 |
| Sylow | C79 ⋊ #7537 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 2 generators on 147 points:
(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)(85,91)(86,97)(87,98)(88,103)(89,107)(92,93)(94,119)(95,121)(96,113)(99,129)(100,132)(101,125)(102,110)(104,138)(105,128)(106,111)(108,136)(109,112)(114,134)(115,133)(116,118)(117,140)(120,144)(122,123)(124,130)(126,127)(131,147)(135,142)(137,141)(139,143)(145,146);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,81,82,83)(84,85)(86,91)(87,102)(88,106)(89,109)(90,96)(92,97)(93,98)(94,103)(95,107)(99,119)(100,121)(101,113)(104,137)(105,135)(108,139)(110,123)(111,122)(112,130)(114,129)(115,132)(116,125)(117,138)(118,128)(120,136)(124,140)(126,134)(127,133)(131,144)(141,147)(142,146)(143,145)Polycyclic presentation:
2^8,79|a^2=d,c^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bc,c^a=ce,e^a=ef,f^a=fg,g^a=gh,c^b=ce,e^b=ef,f^b=fg,g^b=gh,i^b=i^781552 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57445);