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C₂×#12926 #494254

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

Aliases

Subgroups

1078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401450);