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C₂×#12073 #483781

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

Aliases

Subgroups

556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 390977);