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C₂×#60565 #10575096

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

Aliases

Subgroups

7742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482292);