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C₂×#7737 #165689

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

Aliases

Subgroups

1937 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 72885);