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C₂×#19695 #6357269

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

Aliases

Subgroups

2154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6264465);