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C₂×#18197 #6346465

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

Aliases

Subgroups

3944 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)(14,19,15,18)(17,22,26,23);(3,4)(5,7)(6,8)(9,10)(11,13,16,24)(12,17,20,26)(14,23,15,22)(18,21,19,25);(3,5)(4,7)(6,9)(8,10);(11,14,16,15)(12,18,20,19)(13,22,24,23)(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, 6253661);