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C₂×#24745 #6442808

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

Aliases

Subgroups

3036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350004);