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C₂×#12702 #493379

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

Aliases

Subgroups

3354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400575);