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C₂×#60568 #10575099

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

Aliases

Subgroups

7942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482295);