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C₂×#61920 #10578596

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

Aliases

Subgroups

6594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

98 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10485792);