Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7546 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 147 |
| transitive degree | μt(G) = 20224 |
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)(84,85,92,112,87,93,113,140,102,117,143,146,128,136,131,123,89,95,115,142,103,118,99,109,106,122,125,116,129,137,86,91,90,96,97,108,104,119,124,120,133,145,130,144,134,147,100,110,105,121,126,138,127,135,132,139,88,94,114,141,98,107,101,111);(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)(85,91)(86,97)(87,98)(88,102)(89,105)(92,101)(93,116)(94,120)(95,123)(96,111)(99,130)(100,115)(103,134)(104,129)(106,133)(107,108)(109,117)(110,121)(112,137)(113,114)(118,146)(119,141)(122,140)(124,125)(126,131)(127,128)(132,143)(135,144)(136,142)(138,147)(139,145)Polycyclic presentation:
2^8,79|a^2=d,b^2=ceh,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,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, 57469);