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C₂×#1909 #21007

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

Aliases

Subgroups

843 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13995);