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C₂×#12563 #492866

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

Aliases

Subgroups

1658 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)(9,20,23,33)(10,16)(11,28)(12,29)(13,30)(14,19)(15,22,32,24)(17,27)(18,26)(21,34,25,38)(31,36,35,37);(4,6)(7,9,12,24,13,25,26,36,14,23,11,22,10,21,27,37)(8,15,18,33,16,31,29,38,19,32,17,20,30,35,28,34);(7,10,14,13)(8,16,19,30)(9,21,23,25)(11,26,12,27)(15,31,32,35)(17,28,18,29)(20,34,33,38)(22,36,24,37)

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, 400062);