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C₂×#34915 #7628082

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

Aliases

Subgroups

6138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535278);