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C₂×#53090 #8092830

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

Aliases

Subgroups

7476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8000026);