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C₂×#21163 #6371881

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

Aliases

Subgroups

2658 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)(9,14,21,29,19,28,20,35)(10,22,24,30,25,36,23,15)(18,31,34,37,32,38,33,27);(4,6)(7,9,12,21,13,19,11,20)(8,14,16,29,17,28,26,35)(10,18,24,34,25,32,23,33)(15,27,22,31,30,37,36,38);(7,10,11,23,13,25,12,24)(8,15,16,22,17,30,26,36)(9,18,20,33,19,32,21,34)(14,27,29,31,28,37,35,38);(9,19)(14,28)(18,32)(20,21)(27,37)(29,35)(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, 6279077);