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C₂×#62878 #10586212

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

Aliases

Subgroups

34618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493408);