Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13551 |
214 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 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)(82,93)(87,105)(92,115)(94,97)(95,118)(96,119)(104,121)(106,108)(107,131)(116,123)(117,138)(120,124)(122,129)(130,140)(132,133)(139,141);(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)(80,82)(81,87,89,105)(83,97)(84,95)(85,96)(86,93)(88,108,109,106)(90,107,112,131)(91,92,113,115)(94,100)(98,124)(99,104)(101,122)(102,118)(103,119)(110,133,134,132)(111,123,135,116)(114,117,137,138)(120,126)(121,127)(125,130)(128,129)(136,141,143,139)(140,142);(80,81,83,88,84,90,98,110,85,91,99,111,101,114,125,136,86,89,100,109,102,112,126,134,103,113,127,135,128,137,142,143)(82,92,94,116,95,117,120,139,96,105,121,108,122,131,140,133,93,115,97,123,118,138,124,141,119,87,104,106,129,107,130,132)Polycyclic presentation:
2^8,79|a^2=d,b^2=e,d^2=f,f^2=g,g^2=h,b^a=bg,e^a=eh,c^b=ch,d^b=dh,i^b=i^783208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 89755);