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C₂×#21178 #6371904

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

Aliases

Subgroups

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

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

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, 6279100);