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C₂×#43123 #7667289

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

Aliases

Subgroups

6582 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(5,9)(8,10)(12,15)(16,17)(19,20,23,25)(21,22,26,24);(3,4)(5,10)(6,7)(8,9)(11,12,14,15)(13,17,18,16)(19,21,23,26)(20,24,25,22);(4,7)(8,10)(11,13,14,18)(12,16,15,17)(19,22)(20,21)(23,24)(25,26);(3,4)(5,8)(6,7)(9,10)(11,13)(12,16)(14,18)(15,17)(19,21)(20,22)(23,26)(24,25);(3,5)(4,8)(6,9)(7,10)(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, 7574485);