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C₂×#38481 #7635783

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

Aliases

Subgroups

6004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542979);