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C₂×#24249 #6442630

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

Aliases

Subgroups

5088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6349826);