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C₂×#62905 #10586246

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

Aliases

Subgroups

35328 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)(13,18)(14,16)(15,22)(17,21)(19,23)(20,24)(25,26);(3,4,7,6)(5,9,10,8)(11,13)(12,17)(14,18)(15,20)(16,21)(19,24)(22,25)(23,26);(3,5,7,10)(4,8,6,9)(11,12,16,14)(13,18,21,17)(15,19,23,22)(20,25,26,24);(3,6,7,4)(5,9,10,8)(11,14,16,12)(13,18,21,17)(15,22,23,19)(20,25,26,24);(11,13)(12,18)(14,17)(15,20)(16,21)(19,25)(22,24)(23,26);(11,15)(12,19)(13,20)(14,22)(16,23)(17,24)(18,25)(21,26)

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, 10493442);