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C₂×#62994 #10586038

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

Aliases

Subgroups

35096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493234);