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C₂×#12712 #493408

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

Aliases

Subgroups

3316 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400604);