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C₂×#61604 #10577200

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

Aliases

Subgroups

8084 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10484396);