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C₂×#2916 #60112

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

Aliases

Subgroups

1293 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53100);