Finite Group Databasebeta

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C₂×#6437629 #72234729

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• rational
• ambivalent

Aliases

Subgroups

62069 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

(1,2);(3,4)(5,13)(6,10)(7,11)(8,12)(9,16)(14,26)(15,27)(17,24)(18,23)(19,25)(20,29)(21,30)(22,32)(28,33)(31,34);(3,5,8,16)(4,9,12,13)(6,14,18,29)(7,15,19,30)(10,20,23,26)(11,21,25,27)(17,31,32,28)(22,34,24,33);(3,4)(5,9)(6,10)(7,11)(8,12)(13,16)(14,20)(15,21)(17,22)(18,23)(19,25)(24,32)(26,29)(27,30)(28,33)(31,34);(3,6)(4,10)(5,14)(7,17)(8,18)(9,20)(11,24)(12,23)(13,26)(15,28)(16,29)(19,32)(21,34)(22,25)(27,33)(30,31);(3,7)(4,11)(5,15)(6,17)(8,19)(9,21)(10,22)(12,25)(13,27)(14,28)(16,30)(18,32)(20,33)(23,24)(26,34)(29,31)

Conjugacy classes & character table

154 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2), (3,4)(5,13)(6,10)(7,11)(8,12)(9,16)(14,26)(15,27)(17,24)(18,23)(19,25)(20,29)(21,30)(22,32)(28,33)(31,34), (3,5,8,16)(4,9,12,13)(6,14,18,29)(7,15,19,30)(10,20,23,26)(11,21,25,27)(17,31,32,28)(22,34,24,33), (3,4)(5,9)(6,10)(7,11)(8,12)(13,16)(14,20)(15,21)(17,22)(18,23)(19,25)(24,32)(26,29)(27,30)(28,33)(31,34), (3,6)(4,10)(5,14)(7,17)(8,18)(9,20)(11,24)(12,23)(13,26)(15,28)(16,29)(19,32)(21,34)(22,25)(27,33)(30,31), (3,7)(4,11)(5,15)(6,17)(8,19)(9,21)(10,22)(12,25)(13,27)(14,28)(16,30)(18,32)(20,33)(23,24)(26,34)(29,31));