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C₂×#10810 #353514

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

Aliases

Subgroups

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260710);