Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #13708 |
158 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 61 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) = 20224 |
A minimal faithful permutation representation — 3 generators on 151 points:
(1,2)(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)(88,90,91,101)(89,96,95,117)(92,109,105,136)(93,114,106,139)(94,116,107,104)(97,124,118,148)(98,127,119,149)(99,128,115,122)(100,130,129,108)(102,123,120,111)(103,126,132,110)(112,146,137,143)(113,121,138,147)(125,151,140,134)(131,141,135,145)(133,144,142,150);(80,82,83,87)(81,84,85,86)(89,95)(96,117)(97,118)(98,119)(99,115)(100,129)(108,130)(113,138)(121,147)(122,128)(124,148)(125,140)(127,149)(131,135)(134,151)(141,145);(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)(80,81,83,85)(82,86,87,84)(88,89,91,95)(90,100,101,129)(92,108,105,130)(93,113,106,138)(94,115,107,99)(96,120,117,102)(97,123,118,111)(98,126,119,110)(103,134,132,151)(104,135,116,131)(109,127,136,149)(112,145,137,141)(114,124,139,148)(121,146,147,143)(122,133,128,142)(125,144,140,150)Polycyclic presentation:
2^8,79|a^2=d,b^2=dh,c^2=h,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=ef,f^a=fg,g^a=gh,i^a=i^78,e^c=ef,f^c=fg,g^c=gh,i^c=i^783169 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90478);