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C₂×#21000 #6371528

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

Aliases

Subgroups

6170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278724);