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C₂×#8376 #185612

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

Aliases

Subgroups

3584 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 92808);