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C₂×#510 #3413

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

Aliases

Subgroups

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

32 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2145);