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C₂×#33657 #7623059

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

Aliases

Subgroups

1646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530255);