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C₂×#29385 #6461445

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

Aliases

Subgroups

1894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6368641);