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C₂×#3584 #63087

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

Aliases

Subgroups

5429 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 56075);