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C₂×#18064 #6345050

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

Aliases

Subgroups

2096 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252246);