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C₂×#11007 #357492

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

Aliases

Subgroups

4374 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264688);