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C₂×#19318 #6353977

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

Aliases

Subgroups

1782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6261173);