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C₂×#23901 #6437614

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

Aliases

Subgroups

7456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6344810);