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C₂×#12622 #492989

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

Aliases

Subgroups

1844 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

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, 400185);