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C₂×#9502 #201658

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

Aliases

Subgroups

1894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108854);