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C₂×#12624 #492998

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

Aliases

Subgroups

1228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400194);