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C₂×#18199 #6346467

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

Aliases

Subgroups

4030 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6253663);