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C₂×#15072 #608184

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

Aliases

Subgroups

5330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515380);