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C₂×#17397 #6342630

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

Aliases

Subgroups

4914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6249826);