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C₂×#21685 #6373709

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

Aliases

Subgroups

3662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280905);