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C₂×#11602 #481069

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

Aliases

Subgroups

1024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 388265);