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C₂×#21248 #6372026

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

Aliases

Subgroups

5050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279222);