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C₂×#35462 #7628830

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

Aliases

Subgroups

6182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 7536026);