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C₂×#63054 #10586369

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

Aliases

Subgroups

32284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493565);