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C₂×#29387 #6461515

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

Aliases

Subgroups

1846 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6368711);