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C₂×#26164 #6438396

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

Aliases

Subgroups

2812 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345592);