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C₂×#36319 #7629972

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

Aliases

Subgroups

7346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537168);