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C₂×#28242 #6465505

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

Aliases

Subgroups

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(8,13)(9,16)(10,20)(11,14)(18,19)(21,22);(3,4,5,6)(7,8,14,20,12,10,11,13)(9,17,16,21,19,15,18,22);(4,6)(7,9)(8,15)(10,17)(11,18)(12,19)(13,21)(14,16)(20,22);(7,10,11,20,12,8,14,13)(9,17,18,22,19,15,16,21)

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, 6372701);