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C₂×#12952 #494328

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

Aliases

Subgroups

1036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401524);