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C₂×#12953 #494330

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

Aliases

Subgroups

1132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401526);