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C₂×#28139 #6459456

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

Aliases

Subgroups

2792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6366652);