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C₂×#22898 #6381482

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

Aliases

Subgroups

3136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6288678);