Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #9296 |
470 conjugacy classes of subgroups.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 5056 |
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)(81,85)(82,83)(86,87)(88,91,94,107)(89,96,98,104)(90,100,102,116)(92,106,93,105)(95,109,110,118)(97,112,108,111)(99,113,114,119)(101,117,103,115);(81,85)(82,83)(86,87)(88,90)(89,95,98,110)(91,100)(92,101)(93,103)(94,102)(96,109,104,118)(97,99,108,114)(105,115)(106,117)(107,116)(111,119,112,113);(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)(80,81,83,85,84,87,82,86)(88,89,93,97,94,98,92,108)(90,99,103,110,102,114,101,95)(91,104,106,112,107,96,105,111)(100,113,117,109,116,119,115,118)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^78,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=eh,f^c=fgh1756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 66274);