Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C157 ⋊ C4 |
| Sylow | C157 ⋊ #2178 |
146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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:
(1,2,7,3)(4,11,14,8)(5,16,12,6)(9,24,23,17)(10,29,25,15)(13,20,27,21)(18,41,36,30)(19,46,42,28)(22,37,40,34)(26,33,44,38)(31,62,53,47)(32,67,63,45)(35,58,57,51)(39,54,61,55)(43,50,65,59)(48,87,74,68)(49,92,88,66)(52,83,78,72)(56,79,82,76)(60,75,86,80)(64,71,90,84)(69,116,99,93)(70,121,117,91)(73,112,103,97)(77,108,107,101)(81,104,111,105)(85,100,115,109)(89,96,119,113)(94,142,128,122)(95,147,143,120)(98,140,132,126)(102,138,135,130)(106,136,131,134)(110,133,127,137)(114,129,123,139)(118,125,145,141)(124,149,152,146)(144,148,154,150)(151,155,156,153)(158,161,163,175,164,176,179,162)(159,166,167,184,169,185,168,177)(160,171,172,180,174,188,173,178)(165,181,182,187,183,189,186,170);(158,160)(159,165)(161,171)(162,178)(163,172)(164,174)(166,181)(167,182)(168,186)(169,183)(170,177)(173,179)(175,180)(176,188)(184,187)(185,189);(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)(158,159,163,167,164,169,179,168)(160,170,172,181,174,187,173,189)(161,166,175,184,176,185,162,177)(165,180,182,188,183,178,186,171)Polycyclic presentation:
2^7,157|a^2=e,c^2=e,d^2=fg,e^2=g,f^2=g,b^a=bd,d^a=df,f^a=fg,h^a=h^129,d^b=df,f^b=fg,h^c=h^129,h^e=h^156473 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 20909);