Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #8135 |
382 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 179 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) = 20224 |
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)(80,82,83,86)(81,85,84,87)(89,94)(90,96)(95,101)(97,102)(105,110)(109,115)(111,117)(116,119);(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)(81,84)(85,87)(88,90)(89,93)(91,97)(92,96)(94,100)(95,99)(98,102)(101,103)(104,106,107,112,108,113,114,118)(105,109,111,116,110,115,117,119);(80,81)(82,85)(83,84)(86,87)(88,89,91,95,92,94,98,101)(90,93,97,99,96,100,102,103)(104,105)(106,109)(107,111)(108,110)(112,116)(113,115)(114,117)(118,119)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,c^a=cgh,c^b=cg,i^b=i^783208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 60003);