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C₂×#59465 #7666364

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

Aliases

Subgroups

6694 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)(12,15)(13,17)(19,20,24,22)(21,26,25,23);(4,5)(8,9)(11,12,14,15)(13,16,17,18)(19,21)(20,23)(22,26)(24,25);(11,12)(13,16)(14,15)(17,18)(19,20,24,22)(21,23,25,26);(3,5,7,4)(6,9,10,8)(11,12)(13,16)(14,15)(17,18)(19,22,24,20)(21,26,25,23);(3,6,7,10)(4,8,5,9)(11,13,14,17)(12,16,15,18)(19,23,24,26)(20,25,22,21)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573560);