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C₂×#3225 #60796

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

Aliases

Subgroups

1043 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)(12,17)(13,20)(14,16)(18,25)(21,26)(22,24);(3,5,6,10)(4,7,8,9)(11,12)(13,21)(14,23)(15,17)(16,19)(18,22)(20,25)(24,26);(5,10)(7,9)(11,13)(12,18)(14,20)(15,22)(16,24)(17,21)(19,25)(23,26);(4,8)(7,9)(11,14,15,16)(12,19,17,23)(13,20,22,24)(18,25,21,26)

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53784);