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C₂×#23189 #6382758

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

Aliases

Subgroups

3074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6289954);