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C₂×#18556 #6348106

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

Aliases

Subgroups

3106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6255302);