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C₂×#60702 #10575322

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

Aliases

Subgroups

7304 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)(11,12)(13,17)(14,21)(15,24)(16,19)(18,23)(20,25)(22,26);(4,7)(8,10)(11,13,16,15)(12,17,19,24)(14,20,22,23)(18,21,25,26);(11,14,15,23,16,22,13,20)(12,18,17,21,19,25,24,26);(3,5,6,9)(4,8,7,10);(14,22)(18,25)(20,23)(21,26)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482518);