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C₂×#13030 #494546

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

Aliases

Subgroups

1324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,12,8,14,24,28,9,15,6,13,23,32,21,10)(5,16,18,29,19,31,25,30,20,27,17,34,26,33,22,11);(4,10,15,28)(6,21)(7,24)(8,23)(11,27,30,16)(12,14,13,32)(17,22)(18,25)(19,26)(29,31,34,33);(3,5)(4,11)(6,22)(7,25)(8,26)(9,20)(10,27)(12,31)(13,33)(14,34)(15,30)(16,28)(17,21)(18,24)(19,23)(29,32)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401742);