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C₂×#37659 #7635108

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

Aliases

Subgroups

11888 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542304);