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C₂×#24410 #6438010

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

Aliases

Subgroups

4552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345206);