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C₂×#38178 #7635408

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

Aliases

Subgroups

6802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542604);