Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #7541 |
94 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)(81,88)(82,95)(83,86)(84,105)(85,106)(89,116)(90,121)(91,120)(92,124)(93,94)(96,108)(97,115)(98,101)(99,135)(100,128)(102,131)(103,110)(104,113)(107,123)(109,114)(111,112)(117,126)(118,122)(119,139)(125,134)(127,140)(129,133)(130,132)(136,142)(137,143)(138,141);(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)(80,81,83,90,87,93,86,111)(82,94,97,121,101,88,100,112)(84,104,102,137,108,117,107,139)(85,109,103,125,110,140,106,92)(89,115,118,95,120,128,141,98)(91,123,122,96,116,131,138,105)(99,134,129,114,136,124,132,127)(113,142,119,133,126,135,143,130)Polycyclic presentation:
2^8,79|a^2=d,c^2=efh,d^2=h,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,c^b=ceh,d^b=dh,e^b=ef,f^b=fg,g^b=gh1528 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 57458);