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C₂×#25733 #6443091

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

Aliases

Subgroups

5350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6350287);