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C₂×#38390 #7635748

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

Aliases

Subgroups

7592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542944);