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C₂×#11153 #357914

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

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, 265110);