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C₂×#48015 #7703978

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

Aliases

Subgroups

7512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7611174);