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C₂×#53164 #8105652

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

Aliases

Subgroups

7380 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,8,9)(5,7,6,10)(13,17)(16,18)(20,23)(24,26);(4,9)(5,6)(12,15)(16,18)(21,25)(24,26);(3,5,8,6)(4,10,9,7)(11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26);(3,6,8,5)(4,7,9,10)(11,13)(12,16)(14,17)(15,18);(3,7)(4,5)(6,9)(8,10)(11,12)(13,16)(14,15)(17,18)(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, 8012848);