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C₂×#63090 #10586995

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

Aliases

Subgroups

56494 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10494191);