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C₂×#33533 #7622836

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

Aliases

Subgroups

3866 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530032);