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C₂×#52472 #8092149

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

Aliases

Subgroups

7770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7999345);