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C₂×#42595 #7640966

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

Aliases

Subgroups

6984 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7548162);