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C₂×#3022 #60386

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

Aliases

Subgroups

2371 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53374);