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C₂×#12640 #493056

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

Aliases

Subgroups

1190 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400252);