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C₂×#13318 #498824

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

Aliases

Subgroups

1520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 406020);