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C₂×#34898 #7628065

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

Aliases

Subgroups

6078 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)(13,16)(14,18)(15,17);(4,7)(8,10)(11,13,15,14)(12,16,17,18)(19,20)(21,25)(22,23)(24,26);(11,14,15,13)(12,16,17,18)(20,23)(24,25);(19,21,22,26)(20,24,23,25);(3,5,6,9)(4,8,7,10)

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535261);