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C₂×#11013 #357563

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

Aliases

Subgroups

4350 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)(9,17,20,13)(10,14)(11,16)(12,15)(18,35,36,27)(19,33,24,28)(21,38,37,29)(22,31)(23,30)(25,34)(26,32);(7,9)(8,13)(10,21)(11,24)(12,20)(14,29)(15,17)(16,33)(18,22)(19,26)(23,37)(25,36)(27,31)(28,32)(30,38)(34,35);(4,6)(7,10,12,23)(8,14,15,30)(9,18,20,36)(11,25,26,22)(13,27,17,35)(16,34,32,31)(19,37,24,21)(28,38,33,29)

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, 264759);