Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q16×C157 ⋊ C4 |
| Sylow | C157 ⋊ #2141 |
220 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 64 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) = 5024 |
A minimal faithful permutation representation — 3 generators on 189 points:
(1,2,5,10,19,32,49,70,95,124,118,91,116,140,134,101,72,47,67,90,115,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,148,151,144,120,142,137,105,76,51,30,46,65,86,111,131,102,77,56,39,26,15,24,37,54,75,100,129,149,155,157,153,146,139,109,80,55,34,17,29,44,61,82,107,135,106,81,60,43,28,41,58,79,104,133,122,147,154,156,150,141,113,84,59,38,21,8,16,27,40,57,78,103,132,110,85,64,45,62,83,108,136,126,93,121,145,152,143,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,114,89,66,87,112,138,130,97,68,92,119,123,94,69,48,31,18,9,4)(158,161,164,163)(159,166,168,179)(160,170,173,172)(162,174,178,177)(165,180,181,182)(167,175,184,185)(169,183,186,189)(171,187,188,176);(158,160,164,173)(159,165,168,181)(161,172,163,170)(162,176,178,187)(166,182,179,180)(167,183,184,189)(169,185,186,175)(171,174,188,177);(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)(160,169)(161,166)(162,175)(163,179)(164,168)(165,171)(167,177)(170,183)(172,189)(173,186)(174,184)(176,182)(178,185)(180,187)(181,188)Polycyclic presentation:
2^7,157|a^2=e,b^2=g,c^2=g,d^2=fg,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^129,c^b=cg,d^b=df,f^b=fg,h^e=h^156578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20820);