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C₂×#24469 #6437929

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

Aliases

Subgroups

4796 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345125);