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C₂×#3210 #60780

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

Aliases

Subgroups

1093 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53768);