Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #13701 |
180 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 207 |
| transitive degree | μt(G) = 10112 |
A minimal faithful permutation representation — 3 generators on 207 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)(80,83)(81,90)(82,98)(84,105)(85,114)(86,107)(87,106)(88,108)(89,119)(91,124)(92,131)(93,125)(94,104)(95,126)(96,134)(97,141)(99,145)(100,152)(101,147)(102,146)(103,148)(109,165)(110,160)(111,169)(112,161)(113,162)(115,170)(116,158)(117,164)(118,171)(120,176)(121,174)(122,156)(123,175)(127,182)(128,183)(129,157)(130,181)(132,184)(133,163)(135,185)(136,188)(137,186)(138,144)(139,187)(140,191)(142,180)(143,193)(149,196)(150,173)(151,197)(153,200)(154,195)(155,199)(159,167)(166,202)(168,201)(172,203)(177,205)(178,204)(179,194)(189,206)(190,198)(192,207);(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)(80,82,97,140,86,101,111,150,85,100,142,178,115,153,113,118,88,103,127,172,117,155,112,151,87,102,143,192,110,149,84,99)(81,89,109,137,93,121,128,136,92,120,166,189,132,177,130,139,95,123,168,190,133,179,129,138,94,122,167,154,116,135,91,96)(83,98,141,191,107,147,169,173,114,152,180,204,170,200,162,171,108,148,182,203,164,199,161,197,106,146,193,207,160,196,105,145)(90,119,165,186,125,174,183,188,131,176,202,206,184,205,181,187,126,175,201,198,163,194,157,144,104,156,159,195,158,185,124,134);(80,81,88,95)(82,96,103,139)(83,104,108,131)(84,109,113,168)(85,94,87,92)(86,116,117,132)(89,118,123,99)(90,114,126,106)(91,127,130,97)(93,115,133,110)(98,144,148,188)(100,138,102,136)(101,154,155,189)(105,159,162,202)(107,163,164,125)(111,167,112,166)(119,173,175,197)(120,150,122,151)(121,178,179,192)(124,180,181,193)(128,142,129,143)(134,152,187,146)(135,172,177,140)(137,153,190,149)(141,157,182,183)(145,156,171,176)(147,198,199,186)(158,170,184,160)(161,165,169,201)(174,191,194,203)(185,204,205,207)(195,200,206,196)Polycyclic presentation:
2^8,79|a^2=h,b^2=df,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,i^b=i^78,e^c=eh1060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90436);