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C₂×#19750 #6357769

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

Aliases

Subgroups

2394 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6264965);