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C₂×#20884 #6371328

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

Aliases

Subgroups

4646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278524);