Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ #7548 |
62 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)(80,81,88,110,83,90,111,134,99,119,126,132,129,137,97,105,85,92,113,131,100,121,136,142,103,116,140,143,94,104,109,123,86,89,114,138,101,115,95,107,130,135,125,118,127,133,82,87,102,117,93,106,128,141,124,122,84,91,112,139,98,120,96,108);(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)(81,87,89,105)(82,93)(83,98)(84,99)(85,102)(88,109)(90,118,115,132)(91,122,116,142)(92,123,117,108)(94,101)(95,112)(96,114)(97,113)(100,127)(103,130)(104,131,120,106)(107,135,134,119)(110,137,138,133)(111,140)(121,143,141,139)(124,125)(126,136)(128,129)Polycyclic presentation:
2^8,79|a^2=d,b^2=ceg,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,d^b=dh3166 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57474);