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C₂×#33530 #7622833

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

Aliases

Subgroups

3976 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)(7,19)(8,23)(9,13)(10,16)(12,22)(15,31)(17,30)(18,29)(20,25)(21,33)(24,28)(26,32)(27,34);(3,5)(4,10)(6,15)(7,20)(8,24)(9,17)(11,25)(12,28)(13,26)(14,19)(16,22)(18,32)(21,34)(23,27)(29,31)(30,33);(7,21)(12,29)(14,30)(16,32)(18,22)(19,33)(20,34)(28,31);(3,6,9,8)(4,11,13,23)(5,15,17,24)(7,18,21,22)(10,25,26,27)(12,19,29,33)(14,31,30,28)(16,20,32,34)

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, 7530029);