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C₂×#24408 #6438008

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

Aliases

Subgroups

4682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6345204);