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C₂×#13008 #494481

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

Aliases

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401677);