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C₂×#18555 #6348105

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

Aliases

Subgroups

4126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6255301);