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C₂×#38014 #7635200

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

Aliases

Subgroups

7144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542396);