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C₂×#62848 #10586003

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

Aliases

Subgroups

56786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 38 points:

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493199);