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C₂×#17651 #6343756

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

Aliases

Subgroups

3484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250952);