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C₂×#37969 #7635248

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

Aliases

Subgroups

6720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542444);