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C₂×#60765 #10575429

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

Aliases

Subgroups

8424 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)(11,12,15,19)(13,21,23,17)(14,20,16,25)(18,24,26,22);(3,5)(4,7)(6,10)(8,9)(11,13,15,23)(12,17,19,21)(14,24,16,22)(18,25,26,20);(5,10)(7,9)(11,13)(12,18)(14,22)(15,23)(16,24)(17,20)(19,26)(21,25);(4,8)(7,9)(12,19)(17,21)(18,26)(20,25);(11,14,15,16)(12,20,19,25)(13,22,23,24)(17,26,21,18)

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482625);