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C₂×#30435 #7500746

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

Aliases

Subgroups

2726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7407942);