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C₂×#12874 #493916

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

Aliases

Subgroups

1014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,14,9,12,8,24)(5,15,17,28,18,10,23,27)(6,19,21,29,22,11,20,13)(16,25,32,31,33,30,34,26);(3,5)(4,10)(6,16)(7,23)(8,17)(9,18)(11,25)(12,15)(13,26)(14,28)(19,30)(20,32)(21,34)(22,33)(24,27)(29,31);(4,11,12,19)(6,20)(7,8)(10,25,15,30)(13,14,29,24)(16,32)(17,23)(21,22)(26,28,31,27)(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, 401112);