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C₂×#44586 #7669017

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

Aliases

Subgroups

6316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576213);