Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7511 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 2 generators on 143 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(81,87,89,92)(82,93)(88,107,108,104)(90,105,111,114)(91,106,112,115)(94,116)(95,117)(96,103)(109,130,132,127)(110,131,133,128)(113,129,135,136)(118,137)(119,125)(120,126)(134,142,143,141)(138,140);(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)(80,81,82,88,83,90,94,109,84,91,95,110,97,113,118,134,85,92,96,107,98,114,119,130,100,115,120,131,121,136,138,142,86,89,93,108,99,111,116,132,101,112,117,133,122,135,137,143,102,87,103,104,123,105,125,127,124,106,126,128,139,129,140,141)Polycyclic presentation:
2^8,79|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,g^2=h,b^a=bg,d^a=dh,i^a=i^78,c^b=ch3208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57375);