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C₂×#23740 #6432428

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

Aliases

Subgroups

3130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339624);