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C₂×#33830 #7623577

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

Aliases

Subgroups

2270 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530773);