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C₂×#18170 #6346425

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

Aliases

Subgroups

3952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6253621);