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C₂×#60710 #10575333

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

Aliases

Subgroups

7138 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)(12,16)(14,18)(17,22)(19,23)(21,25)(24,26);(4,7)(8,10)(12,17)(16,22)(19,24)(23,26);(11,12,18,22,15,17,14,16)(13,19,25,26,20,24,21,23);(3,5,6,9)(4,8,7,10)(11,13)(12,19)(14,21)(15,20)(16,23)(17,24)(18,25)(22,26);(13,20)(19,24)(21,25)(23,26)

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, 10482529);