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C₂×#62824 #10586172

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

Aliases

Subgroups

35454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493368);