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C₂×#12807 #493735

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

Aliases

Subgroups

1146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400931);