Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #8692 |
358 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 119 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)(80,83)(81,85)(82,87)(84,86)(88,91)(89,96)(90,100)(92,105)(93,108)(94,106)(95,109)(97,111)(98,104)(99,113)(101,116)(102,118)(103,117)(107,112)(110,119)(114,115);(80,82,85,84)(81,86,83,87)(88,90,93,102,94,103,92,101)(89,95,107,114,98,110,97,99)(91,100,108,118,106,117,105,116)(96,109,112,115,104,119,111,113);(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)(80,81,84,87,85,83,82,86)(88,89,93,97,94,98,92,107)(90,99,102,110,103,114,101,95)(91,104,105,111,106,96,108,112)(100,115,116,119,117,113,118,109)Polycyclic presentation:
2^8,79|a^2=f,b^2=dh,d^2=g,e^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,e^c=egh,f^c=fg2230 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 62862);