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C₂×#17217 #845026

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

Aliases

Subgroups

4126 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)(15,16,18,19)(17,20,22,21)(25,29)(27,30);(9,13)(12,14)(16,19)(20,21)(23,24,26,28)(25,30,29,27);(7,8)(9,12)(10,11)(13,14)(15,17)(16,20)(18,22)(19,21)(23,25,26,29)(24,27,28,30);(3,4)(5,6)(7,9)(8,12)(10,13)(11,14)(15,16)(17,21)(18,19)(20,22)(23,24)(25,27)(26,28)(29,30)

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, 752222);