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C₂×#60587 #10575121

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

Aliases

Subgroups

7748 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)(11,12,16,15)(13,20,17,18)(14,22,24,26)(19,25,23,21);(4,7)(8,10)(11,13,16,17)(12,18,15,20)(14,21,24,25)(19,22,23,26);(11,14)(12,19)(13,21)(15,23)(16,24)(17,25)(18,22)(20,26);(3,5,6,9)(4,8,7,10)(11,15,16,12)(13,20,17,18)(14,23,24,19)(21,26,25,22);(11,13,16,17)(12,20,15,18)(14,21,24,25)(19,26,23,22)

Conjugacy classes & character table

122 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482317);