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C₂×#33148 #6629774

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

Aliases

Subgroups

2638 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536970);