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C₂×#19814 #6358157

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

Aliases

Subgroups

1673 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6265353);