Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #8754 |
566 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(80,82,83,87)(81,84,85,86)(88,91)(89,95,96,102)(90,99)(92,104)(93,103)(94,107,98,113)(97,110,111,116)(100,115)(101,114)(105,117)(106,109)(108,118,112,119);(88,90,93,101)(89,94,96,98)(91,99,103,114)(92,105,106,100)(95,107,102,113)(97,112,111,108)(104,117,109,115)(110,119,116,118);(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)(82,86,87,84)(83,85)(88,89,92,97,93,96,106,111)(90,98,100,112,101,94,105,108)(91,102,104,116,103,95,109,110)(99,107,115,118,114,113,117,119)Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=dh,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^78,f^b=fg,e^c=eg,f^c=fh1750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 63093);