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C₂×#61075 #10576079

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483275);