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C₂×#24465 #6437924

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

Aliases

Subgroups

4938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345120);