Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C157 ⋊ #1403 |
112 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 173 |
| transitive degree | μt(G) = 2512 |
A minimal faithful permutation representation — 2 generators on 173 points:
(1,3)(2,6)(4,11)(5,9)(7,10)(8,14)(12,15)(13,16)(17,18)(19,27)(20,21)(22,23)(24,40)(25,26)(28,36)(29,30)(31,32)(33,57)(34,35)(37,53)(38,39)(41,49)(42,43)(44,45)(46,78)(47,48)(50,74)(51,52)(54,70)(55,56)(58,66)(59,60)(61,62)(63,103)(64,65)(67,99)(68,69)(71,95)(72,73)(75,91)(76,77)(79,87)(80,81)(82,83)(84,132)(85,86)(88,128)(89,90)(92,124)(93,94)(96,120)(97,98)(100,116)(101,102)(104,112)(105,106)(107,108)(109,158)(110,111)(113,156)(114,115)(117,154)(118,119)(121,152)(122,123)(125,149)(126,127)(129,145)(130,131)(133,141)(134,135)(136,137)(138,155)(139,140)(142,153)(143,144)(146,150)(147,148)(157,165)(159,164)(160,161)(162,163)(166,171)(167,168)(169,170)(172,173);(1,2,4,8,6,3,10,12)(5,13,15,11,16,9,14,7)(18,19,20,22)(21,24,25,31)(23,28,29,27)(26,33,34,44)(30,37,38,40)(32,41,42,36)(35,46,47,61)(39,50,51,57)(43,54,55,53)(45,58,59,49)(48,63,64,82)(52,67,68,78)(56,71,72,74)(60,75,76,70)(62,79,80,66)(65,84,85,107)(69,88,89,103)(73,92,93,99)(77,96,97,95)(81,100,101,91)(83,104,105,87)(86,109,110,136)(90,113,114,132)(94,117,118,128)(98,121,122,124)(102,125,126,120)(106,129,130,116)(108,133,134,112)(111,138,139,162)(115,142,143,158)(119,146,147,156)(123,150,151,154)(127,153,148,152)(131,155,144,149)(135,157,140,145)(137,159,160,141)(161,166,167,165)(163,168,169,164)(170,172,173,171)Polycyclic presentation:
2^7,157|a^2=d,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^129,d^b=deg,e^b=eg,f^b=fg,h^b=h^156,d^c=dfg,e^c=eg,e^d=eg,h^d=h^156446 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 19632);