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C₂×#20194 #6359546

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

Aliases

Subgroups

1975 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266742);