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C₂×#9921 #234466

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

Aliases

Subgroups

1918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

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

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, 141662);