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C₂×#11109 #357697

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

Aliases

Subgroups

2658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264893);