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C₄×#564 #34355

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

Aliases

Subgroups

900 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 36 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27343);