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C₂×#12910 #494163

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

Aliases

Subgroups

738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401359);