Finite Group Databasebeta

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#2258⋊C₃ #68044

• solvable
• monolithic

Aliases

Splittings

Subgroups

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 128 points:

(1,2,3,9,4,10,15,31,5,11,16,32,20,36,47,69,8,14,19,35,23,39,50,72,26,42,53,75,60,82,93,108)(6,43,18,33,61,38,48,109,25,40,98,74,58,117,92,106,28,46,56,77,64,85,95,112,67,88,101,115,103,120,123,126,7,12,54,34,21,83,49,70,65,41,51,113,59,80,121,107,29,44,57,78,62,86,96,110,68,89,99,116,104,118,124,127,27,13,17,76,22,37,94,71,24,87,52,73,102,81,91,125,30,45,55,79,63,84,97,111,66,90,100,114,105,119,122,128);(1,27,8,28)(2,43,14,44)(3,54,19,55)(4,61,23,62)(5,65,26,66)(6,7,29,30)(9,76,35,77)(10,83,39,84)(11,87,42,88)(12,13,45,46)(15,94,50,95)(16,98,53,99)(17,18,56,57)(20,102,60,103)(21,22,63,64)(24,25,67,68)(31,109,72,110)(32,113,75,114)(33,34,78,79)(36,117,82,118)(37,38,85,86)(40,41,89,90)(47,121,93,122)(48,49,96,97)(51,52,100,101)(58,59,104,105)(69,125,108,126)(70,71,111,112)(73,74,115,116)(80,81,119,120)(91,92,123,124)(106,107,127,128)

Polycyclic presentation:

2,3,2^6|a^2=c,c^2=d,d^2=e,e^2=h,f^2=h,g^2=h,f^b=fgh,g^b=f,g^f=gh

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 620);