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C₂×#23884 #6437573

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

Aliases

Subgroups

6078 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344769);