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C₂×#11098 #357676

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

Aliases

Subgroups

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264872);