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C₂×#10012 #233563

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

Aliases

Subgroups

2136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4)(5,8)(6,9)(7,10)(11,12)(13,19)(14,22)(15,18)(16,20)(17,24)(21,26)(23,25);(4,8)(5,6)(9,10)(11,13)(12,16)(14,23)(15,21)(17,26)(18,25)(19,22)(20,24);(4,9)(5,6)(8,10)(16,25)(19,26)

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, 140759);