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C₂×#11040 #357543

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

Aliases

Subgroups

4406 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)(9,18)(10,23)(11,28)(12,16)(13,17)(14,20)(15,26)(19,36)(21,31)(22,30)(24,35)(25,34)(27,33)(29,37)(32,38);(7,9)(8,14)(10,24)(11,21)(12,20)(13,22)(15,32)(16,30)(17,31)(18,28)(19,25)(23,29)(26,37)(27,38)(33,36)(34,35);(7,10)(8,15)(9,19)(11,25)(12,26)(13,27)(14,29)(16,33)(17,34)(18,35)(20,24)(21,38)(22,37)(23,28)(30,32)(31,36)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264739);