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C₂×#18065 #6345053

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

Aliases

Subgroups

1874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252249);