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C₂×#19749 #6357768

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

Aliases

Subgroups

2426 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6264964);