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C₂×#21164 #6371882

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

Aliases

Subgroups

2682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279078);