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C₂×#54180 #8102294

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

Aliases

Subgroups

7862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009490);