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C₂×#15912 #609693

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

Aliases

Subgroups

5102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 516889);