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C₂×#35197 #7628424

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

Aliases

Subgroups

6942 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535620);