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C₂×#10748 #353433

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

Aliases

Subgroups

4090 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 260629);