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C₂×#37683 #7635128

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

Aliases

Subgroups

11702 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(8,10)(11,12,16,13)(14,19,22,17)(15,18,23,20)(21,25,26,24);(4,6)(12,13)(17,19)(18,20)(24,25);(3,4)(5,6)(7,8,9,10)(11,13,16,12)(14,19,22,17)(15,20,23,18)(21,25,26,24);(11,14,16,22)(12,17,13,19)(15,21,23,26)(18,24,20,25);(3,4)(5,6)(11,15,16,23)(12,18,13,20)(14,21,22,26)(17,24,19,25)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542324);