Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #9304 |
436 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)(80,82,84,83)(81,86,87,85)(88,91,93,103)(89,95,96,110)(90,98,99,113)(92,105,106,102)(94,107,109,118)(97,111,104,101)(100,117,115,114)(108,119,116,112);(80,81,83,85,84,87,82,86)(88,90)(89,94,96,109)(91,98)(92,100)(93,99)(95,107,110,118)(97,108,104,116)(101,112,111,119)(102,114)(103,113)(105,117)(106,115);(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)(81,85)(82,83)(86,87)(88,89)(90,94,99,109)(91,101)(92,104)(93,96)(95,102)(97,106)(98,112,113,119)(100,116,115,108)(103,111)(105,110)(107,117,118,114)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=g,d^2=gh,e^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,d^b=dh,f^b=fh,e^c=eh2701 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 66330);