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C₂×#20389 #6369807

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

Aliases

Subgroups

5814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277003);