Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #12112 |
390 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 390 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:
(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)(81,84)(83,86)(85,87)(88,91)(89,97)(90,103)(92,108)(93,116)(94,109)(95,110)(96,119)(98,122)(99,127)(100,107)(101,123)(102,129)(104,132)(105,134)(106,135)(111,138)(112,140)(113,144)(114,141)(115,142)(117,133)(118,145)(120,146)(121,147)(124,148)(125,149)(126,139)(128,137)(130,150)(131,136)(143,151);(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)(82,84)(83,85)(86,87)(88,90,95,106)(89,96,101,121)(91,103,110,135)(92,112,115,143)(93,105,94,117)(97,119,123,147)(98,124,126,136)(99,120,100,128)(102,125,130,111)(104,113,118,114)(107,137,127,146)(108,140,142,151)(109,133,116,134)(122,148,139,131)(129,149,150,138)(132,144,145,141);(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)(84,87)(88,89,95,101)(90,102,106,130)(91,107,110,127)(92,111,115,125)(93,100,94,99)(96,118,121,104)(97,116,123,109)(98,113,126,114)(103,131,135,148)(105,136,117,124)(108,139,142,122)(112,128,143,120)(119,140,147,151)(129,134,150,133)(132,137,145,146)(138,144,149,141)Polycyclic presentation:
2^8,79|a^2=h,b^2=h,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,i^a=i^78,d^b=df,e^b=eg,f^b=fh,i^b=i^78,d^c=dg,e^c=eh1513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 81723);