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C₂×#3067 #60466

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

Aliases

Subgroups

1325 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

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, 53454);