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C₂×#24030 #6440367

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

Aliases

Subgroups

4364 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6347563);