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C₂×#60592 #10575127

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

Aliases

Subgroups

7802 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)(13,21)(14,17)(15,19)(16,18)(20,24)(22,26)(23,25);(4,7)(8,10)(11,13,15,14)(12,17,19,21)(16,22,24,23)(18,25,20,26);(12,18)(16,24)(17,25)(19,20)(21,26)(22,23);(3,5,6,9)(4,8,7,10)(11,14,15,13)(12,17,19,21)(16,23,24,22)(18,25,20,26);(13,14)(17,21)(22,23)(25,26)

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, 10482323);