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C₂×#13098 #494745

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

Aliases

Subgroups

1978 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401941);