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C₂×#56512 #8099047

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

Aliases

Subgroups

6192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006243);