Finite Group Databasebeta

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C₂×#52985 #8093034

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

Aliases

Subgroups

6154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(5,9)(8,10)(12,15)(13,17)(19,20)(21,25)(22,23)(24,26);(3,4)(5,8)(6,7)(9,10)(20,23)(21,26);(4,7)(8,10)(11,12,14,15)(13,16,17,18)(19,20)(21,24)(22,23)(25,26);(3,4)(5,8)(6,7)(9,10)(11,12)(13,16)(14,15)(17,18)(19,21,22,26)(20,24,23,25);(3,5,6,9)(4,8,7,10)(11,13,14,17)(12,16,15,18)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8000230);