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C₂×#21708 #6373757

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

Aliases

Subgroups

3050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6280953);