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C₂×#11179 #357932

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

Aliases

Subgroups

2498 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265128);