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C₂×#13250 #495239

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

Aliases

Subgroups

1076 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402435);