Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C157 ⋊ #1470 |
204 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 3 generators on 189 points:
(1,2)(3,11)(4,5)(6,7)(8,24)(9,10)(12,20)(13,14)(15,16)(17,41)(18,19)(21,37)(22,23)(25,33)(26,27)(28,29)(30,62)(31,32)(34,58)(35,36)(38,54)(39,40)(42,50)(43,44)(45,46)(47,87)(48,49)(51,83)(52,53)(55,79)(56,57)(59,75)(60,61)(63,71)(64,65)(66,67)(68,116)(69,70)(72,112)(73,74)(76,108)(77,78)(80,104)(81,82)(84,100)(85,86)(88,96)(89,90)(91,92)(93,142)(94,95)(97,140)(98,99)(101,138)(102,103)(105,136)(106,107)(109,133)(110,111)(113,129)(114,115)(117,125)(118,119)(120,121)(122,139)(123,124)(126,137)(127,128)(130,134)(131,132)(141,149)(143,148)(144,145)(146,147)(150,155)(151,152)(153,154)(156,157)(158,161,162,169)(159,164,165,171)(160,167,168,173)(163,170,166,172)(176,182)(179,185)(183,188)(186,189);(158,160,162,168)(159,163,165,166)(161,167,169,173)(164,170,171,172)(174,176)(175,179)(177,183)(178,182)(180,186)(181,185)(184,188)(187,189);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,146)(99,126,127,142)(103,130,131,140)(107,134,135,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,143,144,125)(145,150,151,149)(147,152,153,148)(154,156,157,155)(158,159)(160,166,168,163)(161,164)(162,165)(167,172,173,170)(169,171)(174,175,177,180,178,181,184,187)(176,179,183,186,182,185,188,189)Polycyclic presentation:
2^7,157|a^2=e,b^2=f,c^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^129,c^b=cg,e^b=ef,h^c=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, 19783);