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C₂×#33638 #7623025

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

Aliases

Subgroups

1472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,10)(5,15,17,33)(6,8)(7,19)(11,25,26,29)(12,14)(16,20,22,32)(18,21)(23,27,31,34)(24,30);(3,4,6,10,9,12,8,14)(5,11,16,23,17,26,22,31)(7,13,18,24,21,28,19,30)(15,27,32,25,33,34,20,29);(3,5)(4,11)(6,16)(7,20)(8,22)(9,17)(10,23)(12,26)(13,29)(14,31)(15,18)(19,33)(21,32)(24,27)(25,28)(30,34);(4,12)(10,14)(11,26)(13,28)(23,31)(24,30)(25,29)(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, 7530221);