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C₂×#29854 #6435529

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

Aliases

Subgroups

2500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6342725);