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C₂×#41427 #7639648

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

Aliases

Subgroups

6438 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)(11,12)(13,17)(14,16)(15,18)(19,20,24,25)(21,27,30,26)(22,31,33,23)(28,34,32,29);(4,5)(8,9)(11,12,14,16)(13,15,18,17)(20,25)(23,31)(26,27)(29,34);(3,5,7,4)(6,9,10,8)(11,12)(13,15)(14,16)(17,18)(19,21,24,30)(20,26,25,27)(22,32,33,28)(23,29,31,34);(3,6)(4,8)(5,9)(7,10)(11,13)(12,15)(14,18)(16,17)(19,22)(20,23)(21,28)(24,33)(25,31)(26,34)(27,29)(30,32);(19,23)(20,22)(21,29)(24,31)(25,33)(26,32)(27,28)(30,34)

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, 7546844);