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C₂×#18054 #6345041

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

Aliases

Subgroups

2116 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)(13,17)(14,16)(15,18)(19,22)(20,25)(21,23)(24,26);(12,16)(14,22)(17,23)(18,19)(21,26)(24,25);(3,5,6,10,7,4,8,9)(11,13)(12,17)(14,21)(15,20)(16,23)(18,25)(19,24)(22,26);(4,5)(9,10)(12,18)(13,20)(16,19)(21,26)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252237);