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C₂×#33665 #7623070

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

Aliases

Subgroups

1786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530266);