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D₄×#510 #7623624

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

Aliases

Subgroups

1960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530820);