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C₂×#17400 #6342634

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

Aliases

Subgroups

4978 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)(11,12,15,18,16,19,14,23)(13,17,22,25,20,24,21,26);(3,5)(4,7)(6,10)(8,9)(11,13)(12,17)(14,21)(15,22)(16,20)(18,25)(19,24)(23,26);(13,20)(17,24)(21,22)(25,26);(11,14,16,15)(12,18,19,23)(13,21,20,22)(17,25,24,26)

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, 6249830);