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C₂×#12873 #493914

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

Aliases

Subgroups

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401110);