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C₂×#23892 #6437589

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

Aliases

Subgroups

6069 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344785);