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C₂×#13103 #494756

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

Aliases

Subgroups

1990 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401952);