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C₂×#40381 #7637962

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

Aliases

Subgroups

7712 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545158);