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C₂×#11088 #357763

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

Aliases

Subgroups

2738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264959);