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C₂×#12932 #494272

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

Aliases

Subgroups

1090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401468);