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C₂×#60576 #10575109

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

Aliases

Subgroups

7672 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)(12,17)(13,21)(14,16)(18,25)(22,23)(24,26);(4,7)(8,10)(11,12)(13,18)(14,19)(15,17)(16,20)(21,26)(22,24)(23,25);(11,13,15,22)(12,18,17,24)(14,21,16,23)(19,26,20,25);(3,5,6,9)(4,8,7,10)(11,14,15,16)(12,19,17,20)(13,21,22,23)(18,26,24,25);(12,17)(18,24)(19,20)(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, 10482305);