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C₂×#17167 #844946

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

Aliases

Subgroups

3654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 752142);