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C₂×#12080 #483801

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

Aliases

Subgroups

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 390997);