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C₂×#23813 #6432603

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

Aliases

Subgroups

3082 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6339799);