Finite Group Databasebeta

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C₂×#55057 #8102515

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

Aliases

Subgroups

8278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009711);