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C₂×#61080 #10576103

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

Aliases

Subgroups

10618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483299);