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C₂×#9086 #195939

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

Aliases

Subgroups

1710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 103135);