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C₂×#31417 #7504665

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

Aliases

Subgroups

1965 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7411861);