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C₂×#23870 #6437502

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

Aliases

Subgroups

6492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344698);