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C₂×#33848 #7623597

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

Aliases

Subgroups

2054 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530793);