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C₂×#11001 #357485

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

Aliases

Subgroups

4478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264681);