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C₂×#55063 #8102246

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

Aliases

Subgroups

6088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009442);