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C₂×#12996 #494452

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

Aliases

Subgroups

1456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401648);