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C₂×#45461 #7701997

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

Aliases

Subgroups

6330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7609193);