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C₂×#31070 #7503359

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

Aliases

Subgroups

3760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7410555);