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C₂×#3080 #60483

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

Aliases

Subgroups

1071 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53471);