Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4⋊C8×C157 ⋊ C4 |
| Sylow | C157 ⋊ #1286 |
156 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 5024 |
A minimal faithful permutation representation — 2 generators on 181 points:
(1,2,8,4)(3,6,18,14)(5,7,16,10)(9,12,32,24)(11,17,28,20)(13,15,30,26)(19,22,50,38)(21,31,42,34)(23,25,48,44)(27,29,46,40)(33,36,72,56)(35,49,60,52)(37,39,70,62)(41,47,66,58)(43,45,68,64)(51,54,98,78)(53,71,82,74)(55,57,96,84)(59,69,88,80)(61,63,94,90)(65,67,92,86)(73,76,128,104)(75,97,108,100)(77,79,126,110)(81,95,114,106)(83,85,124,116)(87,93,120,112)(89,91,122,118)(99,102,149,134)(101,127,138,130)(103,105,148,139)(107,125,143,136)(109,111,131,144)(113,123,146,141)(115,117,137,147)(119,121,142,145)(129,132,140,151)(133,135,155,153)(150,152,154,157)(158,159,161,164,162,165,160,163)(166,168,169,176,170,175,177,181)(167,171,173,178,172,174,179,180);(2,3,5,4)(6,9,11,10)(7,13,14,8)(12,19,21,20)(15,23,24,18)(16,17,27,26)(22,33,35,34)(25,37,38,32)(28,31,41,40)(29,43,44,30)(36,51,53,52)(39,55,56,50)(42,49,59,58)(45,61,62,48)(46,47,65,64)(54,73,75,74)(57,77,78,72)(60,71,81,80)(63,83,84,70)(66,69,87,86)(67,89,90,68)(76,99,101,100)(79,103,104,98)(82,97,107,106)(85,109,110,96)(88,95,113,112)(91,115,116,94)(92,93,119,118)(102,129,131,130)(105,133,134,128)(108,127,137,136)(111,132,139,126)(114,125,142,141)(117,138,144,124)(120,123,146,145)(121,143,147,122)(135,150,151,149)(140,152,153,148)(154,156,157,155)(159,163)(160,161)(164,165)(166,167)(168,174,175,171)(169,173)(170,172)(176,180,181,178)(177,179)Polycyclic presentation:
2^7,157|a^2=d,b^2=e,c^2=fg,e^2=f,b^a=bc,c^a=cf,e^a=efg,h^a=h^28,d^b=dg,h^b=h^129,h^d=h^156,h^e=h^156812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 19365);