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C₂×#11035 #357590

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

Aliases

Subgroups

4294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,12,17,13,16,11,28)(9,18,21,33,22,14,20,30)(10,23,27,34,25,15,26,32)(19,29,37,31,36,35,24,38);(7,9,13,22)(8,14,16,18)(10,24,25,37)(11,21,12,20)(15,31,23,38)(17,33,28,30)(19,27,36,26)(29,34,35,32);(4,6)(7,10)(8,15)(9,19)(11,27)(12,26)(13,25)(14,29)(16,23)(17,34)(18,35)(20,37)(21,24)(22,36)(28,32)(30,38)(31,33)

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, 264786);