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C₂×#11126 #357808

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

Aliases

Subgroups

2730 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265004);