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C₂×#62927 #10586270

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

Aliases

Subgroups

34510 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493466);