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C₂×#13076 #494665

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

Aliases

Subgroups

1298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401861);