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C₂×#12949 #494320

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

Aliases

Subgroups

1062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401516);