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C₂×#3396 #61392

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54380);