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C₂×#54396 #8102282

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

Aliases

Subgroups

6234 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

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, 8009478);