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C₂×#40094 #7637829

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

Aliases

Subgroups

6178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545025);