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C₂×#10782 #353461

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

Aliases

Subgroups

4062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

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

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, 260657);