Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #13716 |
168 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 151 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 151 points:
(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)(80,82,83,86)(81,85,84,87)(89,96)(91,105)(92,106)(93,110)(95,113)(97,98)(99,126)(100,120)(101,127)(102,128)(103,132)(107,137)(108,121)(109,118)(111,124)(112,119)(114,115)(116,147)(117,141)(122,138)(123,125)(129,150)(130,142)(131,139)(133,145)(134,140)(135,136)(143,151)(144,146)(148,149);(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)(81,84)(85,87)(88,90,94,104)(89,95,100,117)(91,101,108,130)(92,102,111,133)(93,103,110,132)(96,113,120,141)(97,114,123,144)(98,115,125,146)(99,116,112,134)(105,127,121,142)(106,128,124,145)(107,129,135,148)(109,131,138,151)(118,139,122,143)(119,140,126,147)(136,149,137,150);(80,81)(82,85)(83,84)(86,87)(88,89,94,100)(90,95,104,117)(91,96,108,120)(92,109,111,138)(93,112,110,99)(97,121,123,105)(98,124,125,106)(101,113,130,141)(102,131,133,151)(103,134,132,116)(107,126,135,119)(114,142,144,127)(115,145,146,128)(118,137,122,136)(129,147,148,140)(139,150,143,149)Polycyclic presentation:
2^8,79|a^2=h,b^2=h,c^2=d,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,e^c=ef,f^c=fg,g^c=gh,i^c=i^781531 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90518);