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C₂×#24421 #6437982

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

Aliases

Subgroups

4538 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345178);