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C₂×#33692 #7623141

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

Aliases

Subgroups

1531 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530337);