Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #8781 |
310 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)(81,85,87,86)(88,91)(89,95,96,108)(90,99)(92,103)(93,104)(94,106,98,110)(97,102,109,117)(100,113)(101,114)(105,118)(107,116,111,112)(115,119);(88,90,92,100,93,101,105,115)(89,94,97,107,96,98,109,111)(91,99,103,113,104,114,118,119)(95,106,102,116,108,110,117,112);(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)(80,81,83,86,84,87,82,85)(88,89)(90,98,101,94)(91,102,104,117)(92,97)(93,96)(95,103,108,118)(99,112)(100,111,115,107)(105,109)(106,113)(110,119)(114,116)Polycyclic presentation:
2^8,79|a^2=f,b^2=e,c^2=dh,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^78,f^b=fg,f^c=fg3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 63218);