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C₂×#12946 #494312

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

Aliases

Subgroups

1082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401508);