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C₂×#28299 #6466080

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

Aliases

Subgroups

2130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6373276);