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C₂×#30367 #6433927

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

Aliases

Subgroups

2022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6341123);