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C₂×#11092 #357770

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

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, 264966);