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C₂×#62961 #10586306

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

Aliases

Subgroups

35236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493502);