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C₂×#12951 #494326

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

Aliases

Subgroups

1092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401522);