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C₂×#10348 #238097

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

Aliases

Subgroups

1622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 145293);