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C₂×#3020 #60384

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

Aliases

Subgroups

2355 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53372);