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C₂×#51681 #7707567

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

Aliases

Subgroups

5738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7614763);