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C₂×#36359 #7630013

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

Aliases

Subgroups

6396 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537209);