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C₂×#10014 #233567

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

Aliases

Subgroups

1552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(4,8)(5,9)(6,10)(11,12)(13,20)(14,18)(15,23)(16,19)(17,21)(22,26)(24,25);(3,4,7,5)(6,9,10,8)(11,13,16,22)(12,17,19,25)(14,21,15,24)(18,26,23,20);(3,5,7,4)(6,8,10,9)(11,14,16,15)(12,18,19,23)(13,21,22,24)(17,20,25,26)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 140763);