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C₂×#35911 #7629280

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

Aliases

Subgroups

5718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536476);