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C₂×#578 #3583

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

Aliases

Subgroups

704 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2315);