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C₂×#61644 #10577248

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

Aliases

Subgroups

8358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484444);