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C₂×#10403 #238432

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

Aliases

Subgroups

2052 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 145628);