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C₂×#12930 #494265

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

Aliases

Subgroups

1126 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401461);