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C₂×#9499 #201651

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

Aliases

Subgroups

3058 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108847);