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C₂×#8522 #187799

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

Aliases

Subgroups

3966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4,5,8,6,7,9,10)(11,12)(13,20,22,17)(14,18)(15,19)(16,21,25,23)(24,26);(4,7)(5,9)(11,13)(12,16)(14,23)(15,22)(17,18)(19,25)(20,26)(21,24);(11,13)(12,17)(14,21)(15,22)(16,18)(19,20)(23,24)(25,26)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94995);