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C₂×#13005 #494476

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

Aliases

Subgroups

1392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401672);