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C₂×#11186 #357942

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

Aliases

Subgroups

2538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265138);