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C₂×#10947 #354036

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

Aliases

Subgroups

2834 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 261232);