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C₂×#33637 #7623024

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

Aliases

Subgroups

1500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530220);