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C₂×#12750 #493554

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

Aliases

Subgroups

3280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 400750);