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C₂×#21006 #6371535

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

Aliases

Subgroups

6034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278731);