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C₂×#2148 #33391

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

Aliases

Subgroups

577 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,6,10,8,13,20,12)(5,14,17,28,18,31,15,30)(7,21,19,11,23,27,32,29)(9,22,25,16,26,33,24,34);(3,5)(4,9)(6,15)(7,22)(8,18)(10,24)(11,28)(12,25)(13,26)(14,27)(16,32)(17,20)(19,34)(21,31)(23,33)(29,30);(3,6,8,20)(4,10,13,12)(5,15,18,17)(7,19,23,32)(9,24,26,25)(11,27,29,21)(14,30,31,28)(16,22,34,33)

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, 26379);