Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C79 ⋊ #9088 |
480 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)(88,91,94,106)(89,96,98,112)(90,100,102,117)(92,105,93,104)(95,109,111,115)(97,113,107,103)(99,114,110,119)(101,118,108,116);(80,82,83,87,84,81,85,86)(88,90,92,101,94,102,93,108)(89,95,97,99,98,111,107,110)(91,100,105,118,106,117,104,116)(96,109,113,114,112,115,103,119);(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)(80,81,83,86,84,82,85,87)(88,89)(90,99)(91,103,106,113)(92,107)(93,97)(94,98)(95,101)(96,105,112,104)(100,115,117,109)(102,110)(108,111)(114,116,119,118)Polycyclic presentation:
2^8,79|a^2=f,b^2=df,c^2=g,d^2=g,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^78,e^b=eg,d^c=dg,e^c=eg,f^c=fg2710 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 64986);