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C₂×#11000 #357557

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

Aliases

Subgroups

4438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264753);