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C₂×#12955 #494333

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

Aliases

Subgroups

1098 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401529);