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C₂×#23525 #6431932

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

Aliases

Subgroups

4630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 6339128);