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C₂×#12608 #492954

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

Aliases

Subgroups

1278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400150);