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C₂×#11178 #357931

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

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, 265127);