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C₂×#30436 #7500745

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

Aliases

Subgroups

2758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4)(5,14)(6,10)(7,11)(8,13)(9,17)(12,22)(15,30)(16,24)(18,28)(19,29)(20,25)(21,27)(23,31)(26,33)(32,34);(3,5)(4,9)(6,19)(7,16)(8,18)(10,23)(11,14)(12,28)(13,24)(15,21)(17,22)(20,32)(25,29)(26,30)(27,34)(31,33);(3,6,8,21)(4,10,13,27)(5,15,18,19)(7,20,22,33)(9,23,24,34)(11,25,12,26)(14,29,28,30)(16,31,17,32);(4,11)(5,16)(7,22)(10,25)(12,13)(14,28)(15,31)(17,18)(19,32)(20,33)(26,27)(29,30)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7407941);