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C₄×#1868 #354458

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

Aliases

Subgroups

1534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2,3,4);(5,6,9,13,10,14,20,26)(7,11,17,23,16,22,30,34)(8,12,19,25,18,24,31,35)(15,27,29,36,28,21,32,33);(5,7,9,17,10,16,20,30)(6,11,13,23,14,22,26,34)(8,15,19,29,18,28,31,32)(12,21,25,33,24,27,35,36);(5,8)(6,12)(7,15)(9,19)(10,18)(11,21)(13,25)(14,24)(16,28)(17,29)(20,31)(22,27)(23,33)(26,35)(30,32)(34,36)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261654);