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C₂³×#367 #7622530

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

Aliases

Subgroups

2370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529726);